4.4: Schmerber v. California 384 U.S. 757 (1966)
U.S. Supreme Court
Schmerber v. California, 384 U.S. 757 (1966)
Schmerber v. California
No. 658
Argued April 25, 1966
Decided June 20, 1966
384 U.S. 757
CERTIORARI TO THE APPELLATE DEPARTMENT OF THE
SUPERIOR COURT OF CALIFORNIA, COUNTY OF LOS ANGELES
Syllabus
Petitioner was hospitalized following an accident involving an automobile which he had apparently been driving. A police officer smelled liquor on petitioner’s breath and noticed other symptoms of drunkenness at the accident scene and at the hospital, placed him under arrest, and informed him that he was entitled to counsel, that he could remain silent, and that anything he said would be used against him. At the officer’s direction, a physician took a blood sample from petitioner despite his refusal on advice of counsel to consent thereto. A report of the chemical analysis of the blood, which indicated intoxication, was admitted in evidence over objection at petitioner’s trial for driving while intoxicated. Petitioner was convicted, and the conviction was affirmed by the appellate court, which rejected his claims of denial of due process, of his privilege against self-incrimination, of his right to counsel, and of his right not to be subjected to unreasonable searches and seizures.
Held:
1. Breithaupt v. Abram, 352 U. S. 432 , in which a claim of denial of due process of law was rejected in a similar situation is controlling as to the due process aspect. Pp. 384 U. S. 759 -760.
2. The privilege against self-incrimination is not available to an accused in a case such as this, where there is not even a shadow of compulsion to testify against himself, or otherwise provide the State with evidence of a testimonial or communicative nature. Pp. 384 U. S. 760 -765
3. Petitioner’s limited claim, that he was denied his right to counsel by virtue of the withdrawal of blood over his objection on his counsel’s advice is rejected, since he acquired no right merely because counsel advised that he could assert one. Pp. 384 U. S. 765 -766.
4. In view of the substantial interests in privacy involved, petitioner’s right to be free of unreasonable searches and seizures applies to the withdrawal of his blood, but, under the facts in this case, there was no violation of that right. Pp. 384 U. S. 766 -772.
(a) There was probable cause for the arrest, and the same facts as established probable cause justified the police in requiring
Page 384 U. S. 758
petitioner to submit to a test of his blood alcohol content. In view of the time required to bring petitioner to a hospital, the consequences of delay in making a blood test for alcohol, and the time needed to investigate the accident scene, there was no time to secure a warrant, and the clear indication that, in fact, evidence of intoxication would be found rendered the search an appropriate incident of petitioner’s arrest. Pp. 384 U. S. 770 -771.
(b) The test chosen to measure petitioner’s blood alcohol level was a reasonable one, since it was an effective means of determining intoxication, imposed virtually no risk, trauma or pain, and was performed in a reasonable manner by a physician in a hospital. P. 384 U. S. 771 .
Affirmed.
MR. JUSTICE BRENNAN delivered the opinion of the Court.
Petitioner was convicted in Los Angeles Municipal Court of the criminal offense of driving an automobile while under the influence of intoxicating liquor. [ Footnote 1 ] He had been arrested at a hospital while receiving treatment for injuries suffered in an accident involving the automobile that he had apparently been driving. [ Footnote 2 ] At the direction of a police officer, a blood sample was then withdrawn from petitioner’s body by a physician at the hospital.
The chemical analysis of this sample revealed a percent by weight of alcohol in his blood at the time of the offense which indicated intoxication, and the report of this analysis was admitted in evidence at the trial. Petitioner objected to receipt of this evidence of the analysis on the ground that the blood had been withdrawn despite his refusal, on the advice of his counsel, to consent to the test. He contended that, in that circumstance, the withdrawal of the blood and the admission of the analysis in evidence denied him due process of law under the Fourteenth Amendment, as well as specific guarantees of the Bill of Rights secured against the States by that Amendment: his privilege against self-incrimination under the Fifth Amendment; his right to counsel under the Sixth Amendment; and his right not to be subjected to unreasonable searches and seizures in violation of the Fourth Amendment. The Appellate Department of the California Superior Court rejected these contentions and affirmed the conviction. [ Footnote 3 ] In view of constitutional decisions since we last considered these issues in Breithaupt v. Abram, 352 U. S. 432 — see Escobedo v. Illinois, 378 U. S. 478 ; Malloy v. Hogan, 378 U. S. 1 , and Mapp v. Ohio, 367 U. S. 643 — we granted certiorari. 382 U.S. 971. We affirm.
I
THE DUE PROCESS CLAUSE CLAIM
Breithaupt was also a case in which police officers caused blood to be withdrawn from the driver of an automobile involved in an accident, and in which there was ample justification for the officer’s conclusion that the driver was under the influence of alcohol. There, as here, the extraction was made by a physician in a simple, medically acceptable manner in a hospital environment.
There, however, the driver was unconscious at the time the blood was withdrawn, and hence had no opportunity to object to the procedure. We affirmed the conviction there resulting from the use of the test in evidence, holding that, under such circumstances, the withdrawal did not offend “that sense of justice’ of which we spoke in Rochin v. California, 342 U. S. 165 .” 352 U.S. at 352 U. S. 435 . Breithaupt thus requires the rejection of petitioner’s due process argument, and nothing in the circumstances of this case [ Footnote 4 ] or in supervening events persuades us that this aspect of Breithaupt should be overruled.
II
THE PRIVILEGE AGAINST SELF-INCRIMINATION CLAIM
Breithaupt summarily rejected an argument that the withdrawal of blood and the admission of the analysis report involved in that state case violated the Fifth Amendment privilege of any person not to “be compelled in any criminal case to be a witness against himself,” citing Twining v. New Jersey, 211 U. S. 78 . But that case, holding that the protections of the Fourteenth Amendment do not embrace this Fifth Amendment privilege, has been succeeded by Malloy v. Hogan, 378 U. S. 1 , 378 U. S. 8 . We there held that
“[t]he Fourteenth Amendment secures against state invasion the same privilege that the Fifth Amendment guarantees against federal infringement — the right of a person to remain silent unless he chooses to speak in the unfettered exercise of his own will,
and to suffer no penalty . . . for such silence.”
We therefore must now decide whether the withdrawal of the blood and admission in evidence of the analysis involved in this case violated petitioner’s privilege. We hold that the privilege protects an accused only from being compelled to testify against himself, or otherwise provide the State with evidence of a testimonial or communicative nature, [ Footnote 5 ] and that the withdrawal of blood and use of the analysis in question in this case did not involve compulsion to these ends.
It could not be denied that, in requiring petitioner to submit to the withdrawal and chemical analysis of his blood, the State compelled him to submit to an attempt to discover evidence that might be used to prosecute him for a criminal offense. He submitted only after the police officer rejected his objection and directed the physician to proceed. The officer’s direction to the physician to administer the test over petitioner’s objection constituted compulsion for the purposes of the privilege. The critical question, then, is whether petitioner was thus compelled “to be a witness against himself.” [ Footnote 6 ]
If the scope of the privilege coincided with the complex of values it helps to protect, we might be obliged to conclude that the privilege was violated. In Miranda v. Arizona, ante, at 384 U. S. 460 , the Court said of the interests protected by the privilege:
“All these policies point to one overriding thought: the constitutional foundation underlying the privilege is the respect a government — state or federal — must accord to the dignity and integrity of its citizens. To maintain a ‘fair state-individual balance,’ to require the government ‘to shoulder the entire load,’ . . . to respect the inviolability of the human personality, our accusatory system of criminal justice demands that the government seeking to punish an individual produce the evidence against him by its own independent labors, rather than by the cruel, simple expedient of compelling it from his own mouth.”
The withdrawal of blood necessarily involves puncturing the skin for extraction, and the percent by weight of alcohol in that blood, as established by chemical analysis, is evidence of criminal guilt. Compelled submission fails on one view to respect the “inviolability of the human personality.” Moreover, since it enables the State to rely on evidence forced from the accused, the compulsion violates at least one meaning of the requirement that the State procure the evidence against an accused “by its own independent labors.”
As the passage in Miranda implicitly recognizes, however, the privilege has never been given the full scope which the values it helps to protect suggest. History and a long line of authorities in lower courts have consistently limited its protection to situations in which the State seeks to submerge those values by obtaining the evidence against an accused through
“the cruel, simple expedient of compelling it from his own mouth. . . . In sum, the privilege is fulfilled only when the person is guaranteed the right ‘to remain silent unless he chooses to speak in the unfettered exercise of his own will.'”
Ibid. The leading case in this Court is Holt v. United States, 218 U. S. 245 . There the question was whether evidence was admissible that the accused, prior to trial and over his protest, put on a blouse that fitted him. It was contended that compelling the accused to submit to the demand that he model the blouse violated the privilege. Mr. Justice Holmes, speaking for the Court, rejected the argument as “based upon an extravagant extension of the Fifth Amendment,” and went on to say:
“[T]he prohibition of compelling a man in a criminal court to be witness against himself is a prohibition of the use of physical or moral compulsion to extort communications from him, not an exclusion of his body as evidence when it may be material. The objection in principle would forbid a jury to look at a prisoner and compare his features with a photograph in proof.”
218 U.S. at 218 U. S. 252 -253. [ Footnote 7 ]
It is clear that the protection of the privilege reaches an accused’s communications, whatever form they might take, and the compulsion of responses which are also communications, for example, compliance with a subpoena to produce one’s papers. Boyd v. United States, 116 U. S. 616 . On the other hand, both federal and state courts have usually held that it offers no protection against compulsion to submit to fingerprinting, photographing, or measurements, to write or speak for identification, to appear in court, to stand, to assume a stance, to walk, or to make a particular gesture. [ Footnote 8 ] The distinction which has emerged, often expressed in different ways, is that the privilege is a bar against compelling “communications” or “testimony,” but that compulsion which makes a suspect or accused the source of “real or physical evidence” does not violate it.
Although we agree that this distinction is a helpful framework for analysis, we are not to be understood to agree with past applications in all instances. There will be many cases in which such a distinction is not readily drawn. Some tests seemingly directed to obtain “physical evidence,” for example, lie detector tests measuring changes in body function during interrogation, may actually be directed to eliciting responses which are essentially testimonial. To compel a person to submit to testing in which an effort will be made to determine his guilt or innocence on the basis of physiological responses, whether willed or not, is to evoke the spirit and history of the Fifth Amendment. Such situations call to mind the principle that the protection of the privilege “is as broad as the mischief against which it seeks to guard.” Counselman v. Hitchcock, 142 U. S. 547 , 142 U. S. 562 .
In the present case, however, no such problem of application is presented. Not even a shadow of testimonial compulsion upon or enforced communication by the accused was involved either in the extraction or in the chemical analysis. Petitioner’s testimonial capacities were in no way implicated; indeed, his participation, except as a donor, was irrelevant to the results of the test, which depend on chemical analysis and on that alone. [ Footnote 9 ] Since the blood test evidence, although an incriminating product of compulsion, was neither petitioner’s testimony nor evidence relating to some communicative act or writing by the petitioner, it was not inadmissible on privilege grounds.
III
THE RIGHT TO COUNSEL CLAIM
This conclusion also answers petitioner’s claim that, in compelling him to submit to the test in face of the fact that his objection was made on the advice of counsel, he was denied his Sixth Amendment right to the assistance of counsel. Since petitioner was not entitled to assert the privilege, he has no greater right because counsel erroneously advised him that he could assert it. His claim is strictly limited to the failure of the police to respect his wish, reinforced by counsel’s advice, to be left inviolate. No issue of counsel’s ability to assist petitioner in respect of any rights he did possess is presented. The limited claim thus made must be rejected.
IV
THE SEARCH AND SEIZURE CLAIM
In Breithaupt, as here, it was also contended that the chemical analysis should be excluded from evidence as the product of an unlawful search and seizure in violation of the Fourth and Fourteenth Amendments. The Court did not decide whether the extraction of blood in that case was unlawful, but rejected the claim on the basis of Wolf v. Colorado, 338 U. S. 25 . That case had held that the Constitution did not require, in state prosecutions for state crimes, the exclusion of evidence obtained in violation of the Fourth Amendment’s provisions. We have since overruled Wolf in that respect, holding in Mapp v. Ohio, 367 U. S. 643 , that the exclusionary rule adopted for federal prosecutions in Weeks v. United States, 232 U. S. 383 , must also be applied in criminal prosecutions in state courts. The question is squarely presented therefore, whether the chemical analysis introduced in evidence in this case should have been excluded as the product of an unconstitutional search and seizure.
The overriding function of the Fourth Amendment is to protect personal privacy and dignity against unwarranted intrusion by the State. In Wolf, we recognized “[t]he security of one’s privacy against arbitrary intrusion by the police” as being “at the core of the Fourth Amendment” and “basic to a free society.” 338 U.S. at 338 U. S. 27 . We reaffirmed that broad view of the Amendment’s purpose in applying the federal exclusionary rule to the States in Mapp.
The values protected by the Fourth Amendment thus substantially overlap those of the Fifth Amendment helps to protect. History and precedent have required that we today reject the claim that the Self-Incrimination Clause of the Fifth Amendment requires the human body in all circumstances to be held inviolate against state expeditions seeking evidence of crime. But if compulsory administration of a blood test does not implicate the Fifth Amendment, it plainly involves the broadly conceived reach of a search and seizure under the Fourth Amendment. That Amendment expressly provides that “[t]he right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated. . . .” (Emphasis added.) It could not reasonably be argued, and indeed respondent does not argue, that the administration of the blood test in this case was free of the constraints of the Fourth Amendment. Such testing procedures plainly constitute searches of “persons,” and depend antecedently upon seizures of “persons,” within the meaning of that Amendment.
Because we are dealing with intrusions into the human body, rather than with state interferences with property relationships or private papers — “houses, papers, and effects” — we write on a clean slate. Limitations on the kinds of property which may be seized under warrant, [ Footnote 10 ] as distinct from the procedures for search and the permissible scope of search, [ Footnote 11 ] are not instructive in this context. We begin with the assumption that, once the privilege against self-incrimination has been found not to bar compelled intrusions into the body for blood to be analyzed for alcohol contest, the Fourth Amendment’s proper function is to constrain not against all intrusions as such, but against intrusions which are not justified in the circumstances, or which are made in an improper manner. In other words, the questions we must decide in this case are whether the police were justified in requiring petitioner to submit to the blood test, and whether the means and procedures employed in taking his blood respected relevant Fourth Amendment standards of reasonableness.
In this case, as will often be true when charges of driving under the influence of alcohol are pressed, these questions arise in the context of an arrest made by an officer without a warrant. Here, there was plainly probable cause for the officer to arrest petitioner and charge him with driving an automobile while under the influence of intoxicating liquor. [ Footnote 12 ] The police officer who arrived at the scene shortly after the accident smelled liquor on petitioner’s breath, and testified that petitioner’s eyes were “bloodshot, watery, sort of a glassy appearance.” The officer saw petitioner again at the hospital, within two hours of the accident. There, he noticed similar symptoms of drunkenness. He thereupon informed petitioner
“that he was under arrest and that he was entitled to the services of an attorney, and that he could remain silent, and that anything that he told me would be used against him in evidence.”
While early cases suggest that there is an unrestricted
“right on the part of the government, always recognized under English and American law, to search the person of the accused when legally arrested, to discover and seize the fruits or evidences of crime,”
Weeks v. United States, 232 U. S. 383 , 232 U. S. 392 ; People v. Chiagles, 237 N.Y. 193, 142 N.E. 583 (1923) (Cardozo, J.), the mere fact of a lawful arrest does not end our inquiry. The suggestion of these cases apparently rests on two factors — first, there may be more immediate danger of concealed weapons or of destruction of evidence under the direct control of the accused, United States v. Rabinowitz, 339 U. S. 56 , 339 U. S. 72 -73 (Frankfurter, J., dissenting); second, once a search of the arrested person for weapons is permitted, it would be both impractical and unnecessary to enforcement of the Fourth Amendment’s purpose to attempt to confine the search to those objects alone. People v. Chiagles, 237 N.Y. at 197-198, 142 N.E. at 584. Whatever the validity of these considerations in general, they have little applicability with respect to searches involving intrusions beyond the body’s surface. The interests in
Page 384 U. S. 770
human dignity and privacy which the Fourth Amendment protects forbid any such intrusions on the mere chance that desired evidence might be obtained. In the absence of a clear indication that in fact such evidence will be found, these fundamental human interests require law officers to suffer the risk that such evidence may disappear unless there is an immediate search.
Although the facts which established probable cause to arrest in this case also suggested the required relevance and likely success of a test of petitioner’s blood for alcohol, the question remains whether the arresting officer was permitted to draw these inferences himself, or was required instead to procure a warrant before proceeding with the test. Search warrants are ordinarily required for searches of dwellings, and, absent an emergency, no less could be required where intrusions into the human body are concerned. The requirement that a warrant be obtained is a requirement that inferences to support the search
“be drawn by a neutral and detached magistrate instead of being judged by the officer engaged in the often competitive enterprise of ferreting out crime.”
Johnson v. United States, 333 U. S. 10 , 333 U. S. 13 -14; see also Aguilar v. Texas, 378 U. S. 108 , 378 U. S. 110 -111. The importance of informed, detached and deliberate determinations of the issue whether or not to invade another’s body in search of evidence of guilt is indisputable and great.
The officer in the present case, however, might reasonably have believed that he was confronted with an emergency, in which the delay necessary to obtain a warrant, under the circumstances, threatened “the destruction of evidence,” Preston v. United States, 376 U. S. 364 , 376 U. S. 367 . We are told that the percentage of alcohol in the blood begins to diminish shortly after drinking stops, as the body functions to eliminate it from the system. Particularly in a case such as this, where time had to be taken to bring the accused to a hospital and to investigate the scene of the accident, there was no time to seek out a magistrate and secure a warrant. Given these special facts, we conclude that the attempt to secure evidence of blood alcohol content in this case was an appropriate incident to petitioner’s arrest.
Similarly, we are satisfied that the test chosen to measure petitioner’s blood alcohol level was a reasonable one. Extraction of blood samples for testing is a highly effective means of determining the degree to which a person is under the influence of alcohol. See Breithaupt v. Abram, 352 U.S. at 352 U. S. 436 , n. 3. Such tests are a commonplace in these days of periodic physical examination, [ Footnote 13 ] and experience with them teaches that the quantity of blood extracted is minimal, and that, for most people, the procedure involves virtually no risk, trauma, or pain. Petitioner is not one of the few who on grounds of fear, concern for health, or religious scruple might prefer some other means of testing, such as the “Breathalyzer” test petitioner refused, see n 9, supra. We need not decide whether such wishes would have to be respected. [ Footnote 14 ]
Finally, the record shows that the test was performed in a reasonable manner. Petitioner’s blood was taken by a physician in a hospital environment according to accepted medical practices. We are thus not presented with the serious questions which would arise if a search involving use of a medical technique, even of the most rudimentary sort, were made by other than medical personnel or in other than a medical environment — for example, if it were administered by police in the privacy of the stationhouse. To tolerate searches under these conditions might be to invite an unjustified element of personal risk of infection and pain.
We thus conclude that the present record shows no violation of petitioner’s right under the Fourth and Fourteenth Amendments to be free of unreasonable searches and seizures. It bears repeating, however, that we reach this judgment only on the facts of the present record. The integrity of an individual’s person is a cherished value of our society. That we today told that the Constitution does not forbid the States minor intrusions into an individual’s body under stringently limited conditions in no way indicates that it permits more substantial intrusions, or intrusions under other conditions.
Affirmed.
[ Footnote 1 ]
California Vehicle Code § 23102(a) provides, in pertinent part, “It is unlawful for any person who is under the influence of intoxicating liquor . . . to drive a vehicle upon any highway. . . .” The offense is a misdemeanor.
[ Footnote 2 ]
Petitioner and a companion had been drinking at a tavern and bowling alley. There was evidence showing that petitioner was driving from the bowling alley about midnight November 12, 1964, when the car skidded, crossed the road and struck a tree. Both petitioner and his companion were injured and taken to a hospital for treatment.
[ Footnote 3 ]
This was the judgment of the highest court of the State in this proceeding since certification to the California District Court of Appeal was denied. See Edwards v. California, 314 U. S. 160 .
[ Footnote 4 ]
We
“cannot see that it should make any difference whether one states unequivocally that he objects or resorts to physical violence in protest or is in such condition that he is unable to protest.”
Breithaupt v. Abram, 352 U.S. at 352 U. S. 441 . (WARREN, C.J., dissenting). It would be a different case if the police initiated the violence, refused to respect a reasonable request to undergo a different form of testing, or responded to resistance with inappropriate force. Compare the discussion at 384 U. S. infra.
[ Footnote 5 ]
A dissent suggests that the report of the blood test was “testimonial” or “communicative,” because the test was performed in order to obtain the testimony of others, communicating to the jury facts about petitioner’s condition. Of course, all evidence received in court is “testimonial” or “communicative” if these words are thus used. But the Fifth Amendment relates only to acts on the part of the person to whom the privilege applies, and we use these words subject to the same limitations. A nod or headshake is as much a “testimonial” or “communicative” act in this sense as are spoken words. But the terms as we use them do not apply to evidence of acts noncommunicative in nature as to the person asserting the privilege, even though, as here, such acts are compelled to obtain the testimony of others.
[ Footnote 6 ]
Many state constitutions, including those of most of the original Colonies, phrase the privilege in terms of compelling a person to give “evidence” against himself. But our decision cannot turn on the Fifth Amendment’s use of the word “witness.”
“[A]s the manifest purpose of the constitutional provisions, both of the states and of the United States, is to prohibit the compelling of testimony of a self-incriminating kind from a party or a witness, the liberal construction which must be placed upon constitutional provisions for the protection of personal rights would seem to require that the constitutional guaranties, however differently worded, should have as far as possible the same interpretation. . . .”
Counselman v. Hitchcock, 142 U. S. 547 , 142 U. S. 584 -585. 8 Wigmore, Evidence § 2252 (McNaughton rev. 1961).
[ Footnote 7 ]
Compare Wigmore’s view,
“that the privilege is limited to testimonial disclosures. It was directed at the employment of legal process to extract from the person’s own lips an admission of guilt, which would thus take the place of other evidence.”
8 Wigmore, Evidence § 2263 (McNaughton rev. 1961). California adopted the Wigmore formulation in People v. Trujillo, 32 Cal.2d 105, 194 P.2d 681 (1948); with specific regard to blood tests, see People v. Haeussler, 41 Cal.2d 252, 260 P.2d 8 (1953); People v. Duroncelay, 48 Cal.2d 766, 312 P.2d 690 (1957). Our holding today, however, is not to be understood as adopting the Wigmore formulation.
[ Footnote 8 ]
The cases are collected in 8 Wigmore, Evidence § 2265 (McNaughton rev. 1961). See also United States v. Chibbaro, 361 F.2d 365 (C.A.3d Cir. 1966); People v. Graves, 64 Cal.2d 208, 49 Cal.Rptr. 386, 388, 411 P.2d 114, 116 (1966); Weintraub, Voice Identification, Writing Exemplars and the Privilege Against Self-Incrimination, 10 Vand.L.Rev. 485 (1957).
[ Footnote 9 ]
This conclusion would not necessarily govern had the State tried to show that the accused had incriminated himself when told that he would have to be tested. Such incriminating evidence may be an unavoidable by-product of the compulsion to take the test, especially for an individual who fears the extraction or opposes it on religious grounds. If it wishes to compel persons to submit to such attempts to discover evidence, the State may have to forgo the advantage of any testimonial products of administering the test — products which would fall within the privilege. Indeed, there may be circumstances in which the pain, danger, or severity of an operation would almost inevitably cause a person to prefer confession to undergoing the “search,” and nothing we say today should be taken as establishing the permissibility of compulsion in that case. But no such situation is presented in this case. See text at n 13 infra.
Petitioner has raised a similar issue in this case in connection with a police request that he submit to a “breathalyzer” test of air expelled from his lungs for alcohol content. He refused the request, and evidence of his refusal was admitted in evidence without objection. He argues that the introduction of this evidence and a comment by the prosecutor in closing argument upon his refusal is ground for reversal under Griffin v. California, 380 U. S. 609 . We think general Fifth Amendment principles, rather than the particular holding of Griffin, would be applicable in these circumstances, see Miranda v. Arizona, ante at 384 U. S. 468 , n. 37. Since trial here was conducted after our decision in Malloy v. Hogan, supra, making those principles applicable to the States, we think petitioner’s contention is foreclosed by his failure to object on this ground to the prosecutor’s question and statements.
[ Footnote 10 ]
See, e.g., Gouled v. United States, 255 U. S. 298 ; Boyd v. United States, 116 U. S. 616 ; contra, People v. Thayer, 63 Cal.2d 635, 47 Cal.Rptr. 780, 408 P.2d 108 (1965); State v. Bisaccia, 45 N.J. 504, 213 A.2d 185 (1965); Note, Evidentiary Searches: The Rule and the Reason, 54 Geo.L.J. 593 (1966).
[ Footnote 11 ]
See, e.g. Silverman v. United States, 365 U. S. 505 ; Abel v. United States, 362 U. S. 217 , 362 U. S. 235 ; United States v. Rabinowitz, 339 U. S. 56 .
[ Footnote 12 ]
California law authorizes a peace officer to arrest
“without a warrant . . . [w]henever he has reasonable cause to believe that the person to be arrested has committed a felony, whether or not a felony has in fact been committed.”
Cal.Penal Code § 836.3. Although petitioner was ultimately prosecuted for a misdemeanor he was subject to prosecution for the felony since a companion in his car was injured in the accident, which apparently was the result of traffic law violations. Cal.Vehicle Code § 23101. California’s test of probable cause follows the federal standard. People v. Cockrell, 63 Cal.2d 659, 47 Cal.Rptr. 788, 408 P.2d 116 (1965).
[ Footnote 13 ]
The blood test procedure has become routine in our everyday life. It is a ritual for those going into military service, as well as those applying for marriage licenses. Many colleges require such tests before permitting entrance, and literally millions of us have voluntarily gone through the same, though a longer, routine in becoming blood donors.
Breithaupt v. Abram, 352 U.S. at 352 U. S. 436 .
[ Footnote 14 ]
See Karst, Legislative Facts in Constitutional Litigation, 1960 Sup.Ct.Rev. 75, 82-83.
MR. JUSTICE HARLAN, whom MR. JUSTICE STEWART joins, concurring.
In joining the Court’s opinion, I desire to add the following comment. While agreeing with the Court that the taking of this blood test involved no testimonial compulsion, I would go further and hold that, apart from this consideration, the case in no way implicates the Fifth Amendment. Cf. my dissenting opinion and that of MR. JUSTICE WHITE in Miranda v. Arizona, ante, pp. 384 U. S. 504 , 384 U. S. 526 .
MR. CHIEF JUSTICE WARREN, dissenting.
While there are other important constitutional issues in this case, I believe it is sufficient for me to reiterate my dissenting opinion in Breithaupt v. Abram, 352 U. S. 432 , 352 U. S. 440 , as the basis on which to reverse this conviction.
Page 384 U. S. 773
MR. JUSTICE BLACK with whom MR. JUSTICE DOUGLAS joins, dissenting.
I would reverse petitioner’s conviction. I agree with the Court that the Fourteenth Amendment made applicable to the States the Fifth Amendment’s provision that “No person . . . shall be compelled in any criminal case to be a witness against himself. . . .” But I disagree with the Court’s holding that California did not violate petitioner’s constitutional right against self-incrimination when it compelled him, against his will, to allow a doctor to puncture his blood vessels in order to extract a sample of blood and analyze it for alcoholic content, and then used that analysis as evidence to convict petitioner of a crime.
The Court admits that
“the State compelled [petitioner] to submit to an attempt to discover evidence [in his blood] that might be [and was] used to prosecute him for a criminal offense.”
To reach the conclusion that compelling a person to give his blood to help the State convict him is not equivalent to compelling him to be a witness against himself strikes me as quite an extraordinary feat. The Court, however, overcomes what had seemed to me to be an insuperable obstacle to its conclusion by holding that
“. . . the privilege protects an accused only from being compelled to testify against himself, or otherwise provide the State with evidence of a testimonial or communicative nature, and that the withdrawal of blood and use of the analysis in question in this case did not involve compulsion to these ends.”
(Footnote omitted.) I cannot agree that this distinction and reasoning of the Court justify denying petitioner his Bill of Rights’ guarantee that he must not be compelled to be a witness against himself.
In the first place, it seems to me that the compulsory extraction of petitioner’s blood for analysis so that the person who analyzed it could give evidence to convict him had both a “testimonial” and a “communicative nature.” The sole purpose of this project, which proved to be successful, was to obtain “testimony” from some person to prove that petitioner had alcohol in his blood at the time he was arrested. And the purpose of the project was certainly “communicative” in that the analysis of the blood was to supply information to enable a witness to communicate to the court and jury that petitioner was more or less drunk
I think it unfortunate that the Court rests so heavily for its very restrictive reading of the Fifth Amendment’s privilege against self-incrimination on the words “testimonial” and “communicative.” These words are not models of clarity and precision, as the Court’s rather labored explication shows. Nor can the Court, so far as I know, find precedent in the former opinions of this Court for using these particular words to limit the scope of the Fifth Amendment’s protection. There is a scholarly precedent, however, in the late Professor Wigmore’s learned treatise on evidence. He used “testimonial” which, according to the latest edition of his treatise revised by McNaughton, means “communicative” (8 Wigmore, Evidence § 2263 (McNaughton rev. 1961), p. 378), as a key word in his vigorous and extensive campaign designed to keep the privilege against self-incrimination “within limits the strictest possible.” 8 Wigmore, Evidence § 2251 (3d ed. 1940), p. 318. Though my admiration for Professor Wigmore’s scholarship is great, I regret to see the word he used to narrow the Fifth Amendment’s protection play such a major part in any of this Court’s opinions.
I am happy that the Court itself refuses to follow Professor Wigmore’s implication that the Fifth Amendment goes no further than to bar the use of forced self-incriminating statements coming from a “person’s own lips.” It concedes, as it must so long as Boyd v. United States, 116 U. S. 616 , stands, that the Fifth Amendment bars a State from compelling a person to produce papers he has that might tend to incriminate him. It is a strange hierarchy of values that allows the State to extract a human being’s blood to convict him of a crime because of the blood’s content, but proscribes compelled production of his lifeless papers. Certainly there could be few papers that would have any more “testimonial” value to convict a man of drunken driving than would an analysis of the alcoholic content of a human being’s blood introduced in evidence at a trial for driving while under the influence of alcohol. In such a situation, blood, of course, is not oral testimony given by an accused, but it can certainly “communicate” to a court and jury the fact of guilt.
The Court itself, at page 384 U. S. 764 , expresses its own doubts, if not fears, of its own shadowy distinction between compelling “physical evidence” like blood which it holds does not amount to compelled self-incrimination, and “eliciting responses which are essentially testimonial.” And, in explanation of its fears, the Court goes on to warn that
“To compel a person to submit to testing [by lie detectors, for example] in which an effort will be made to determine his guilt or innocence on the basis of physiological responses, whether willed or not, is to evoke the spirit and history of the Fifth Amendment. Such situations call to mind the principle that the protection of the privilege ‘is as broad as the mischief against which it seeks to guard.’ Counselman v. Hitchcock, 142 U. S. 547 , 142 U. S. 562 .”
A basic error in the Court’s holding and opinion is its failure to give the Fifth Amendment’s protection against compulsory self-incrimination the broad and liberal construction that Counselman and other opinions of this Court have declared it ought to have.
The liberal construction given the Bill of Rights’ guarantee in Boyd v. United States, supra, which Professor Wigmore criticized severely, see 8 Wigmore, Evidence, § 2264 (3d ed. 1940), pp. 366-373, makes that one among the greatest constitutional decisions of this Court. In that case, 116 U.S. at 116 U. S. 634 -635, all the members of the Court decided that civil suits for penalties and forfeitures incurred for commission of offenses against the law,
“. . . are within the reason of criminal proceedings for all the purposes of . . . that portion of the fifth amendment which declares that no person shall be compelled in any criminal case to be a witness against himself; . . . within the meaning of the fifth amendment to the constitution. . . . * ”
Obviously, the Court’s interpretation was not completely supported by the literal language of the Fifth Amendment. Recognizing this, the Court announced a rule of constitutional interpretation that has been generally followed ever since, particularly in judicial construction of Bill of Rights guarantees:
“A close and literal construction [of constitutional provisions for the security of persons and property] deprives them of half their efficacy, and leads to gradual depreciation of the right, as if it consisted more in sound than in substance. It is the duty of courts to be watchful for the constitutional rights of the citizen, and against any stealthy encroachments thereon.”
Boyd v. United States, supra, at 116 U. S. 635 .
The Court went on to say, at 116 U. S. 637 , that to require
“an owner to produce his private books and papers, in order to prove his breach of the laws, and thus to establish the forfeiture of his property, is surely compelling him to furnish evidence against himself.”
The Court today departs from the teachings of Boyd. Petitioner Schmerber has undoubtedly been compelled to give his blood “to furnish evidence against himself,” yet the Court holds that this is not forbidden by the Fifth Amendment. With all deference, I must say that the Court here gives the Bill of Rights’ safeguard against compulsory self-incrimination a construction that would generally be considered too narrow and technical even in the interpretation of an ordinary commercial contract.
The Court apparently, for a reason I cannot understand, finds some comfort for its narrow construction of the Fifth Amendment in this Court’s decision in Miranda v. Arizona, ante, p. 384 U. S. 436 . I find nothing whatever in the majority opinion in that case which either directly or indirectly supports the holding in this case. In fact, I think the interpretive constitutional philosophy used in Miranda, unlike that used in this case, gives the Fifth Amendment’s prohibition against compelled self-incrimination a broad and liberal construction in line with the wholesome admonitions in the Boyd case. The closing sentence in the Fifth Amendment section of the Court’s opinion in the present case is enough by itself, I think, to expose the unsoundness of what the Court here holds. That sentence reads:
“Since the blood test evidence, although an incriminating product of compulsion, was neither petitioner’s testimony nor evidence relating to some communicative act or writing by the petitioner, it was not inadmissible on privilege grounds. ”
How can it reasonably be doubted that the blood test evidence was not in all respects the actual equivalent of “testimony” taken from petitioner when the result of the test was offered as testimony, was considered by the jury as testimony, and the jury’s verdict of guilt rests in part on that testimony? The refined, subtle reasoning and balancing process used here to narrow the scope of the Bill of Rights’ safeguard against self-incrimination provides a handy instrument for further narrowing of that constitutional protection, as well as others, in the future. Believing with the Framers that these constitutional safeguards broadly construed by independent tribunals of justice provide our best hope for keeping our people free from governmental oppression, I deeply regret the Court’s holding. For the foregoing reasons, as well as those set out in concurring opinions of BLACK and DOUGLAS, JJ., in Rochin v. California, 342 U. S. 165 , 342 U. S. 174 , 342 U. S. 177 , and my concurring opinion in Mapp v. Ohio, 367 U. S. 643 , 367 U. S. 661 , and the dissenting opinions in Breithaupt v. Abram, 352 U. S. 432 , 352 U. S. 440 , 352 U. S. 442 , I dissent from the Court’s holding and opinion in this case.
* A majority of the Court applied the same constitutional interpretation to the search and seizure provisions of the Fourth Amendment over the dissent of Mr. Justice Miller, concurred in by Chief Justice Waite.
MR. JUSTICE DOUGLAS, dissenting.
I adhere to the views of THE CHIEF JUSTICE in his dissent in Breithaupt v. Abram, 352 U. S. 432 , 352 U. S. 440 , and to the views I stated in my dissent in that case ( id., 352 U. S. 442 ), and add only a word.
We are dealing with the right of privacy which, since the Breithaupt case, we have held to be within the penumbra of some specific guarantees of the Bill of Rights. Griswold v. Connecticut, 381 U. S. 479 . Thus, the Fifth Amendment marks “a zone of privacy” which the Government may not force a person to surrender. Id., 381 U. S. 484 . Likewise the Fourth Amendment recognizes that right when it guarantees the right of the people to be secure “in their persons.” Ibid. No clearer invasion of this right of privacy can be imagined than forcible bloodletting of the kind involved here.
MR. JUSTICE FORTAS, dissenting.
I would reverse. In my view, petitioner’s privilege against self-incrimination applies. I would add that, under the Due Process Clause, the State, in its role as prosecutor, has no right to extract blood from an accused or anyone else, over his protest. As prosecutor, the State has no right to commit any kind of violence upon the person, or to utilize the results of such a tort, and the extraction of blood, over protest, is an act of violence. Cf. CHIEF JUSTICE WARREN’s dissenting opinion in Breithaupt v. Abram, 352 U. S. 432 , 352 U. S. 440 .
Contributors and Attributions
- Authored by : US Government . Located at : https://supreme.justia.com/cases/federal/us/384/757/case.html . License : Public Domain: No Known Copyright


30.3: Bohr’s Theory of the Hydrogen Atom
Learning Objectives
By the end of this section, you will be able to:
- Describe the mysteries of atomic spectra.
- Explain Bohr’s theory of the hydrogen atom.
- Explain Bohr’s planetary model of the atom.
- Illustrate energy state using the energy-level diagram.
- Describe the triumphs and limits of Bohr’s theory.
The great Danish physicist Niels Bohr (1885–1962) made immediate use of Rutherford’s planetary model of the atom. (Figure \(\PageIndex{1}\)). Bohr became convinced of its validity and spent part of 1912 at Rutherford’s laboratory. In 1913, after returning to Copenhagen, he began publishing his theory of the simplest atom, hydrogen, based on the planetary model of the atom. For decades, many questions had been asked about atomic characteristics. From their sizes to their spectra, much was known about atoms, but little had been explained in terms of the laws of physics. Bohr’s theory explained the atomic spectrum of hydrogen and established new and broadly applicable principles in quantum mechanics.
Mysteries of Atomic Spectra
As noted in "Quantization of Energy," the energies of some small systems are quantized. Atomic and molecular emission and absorption spectra have been known for over a century to be discrete (or quantized) (Figure \(\PageIndex{2}\)). Maxwell and others had realized that there must be a connection between the spectrum of an atom and its structure, something like the resonant frequencies of musical instruments. But, in spite of years of efforts by many great minds, no one had a workable theory. (It was a running joke that any theory of atomic and molecular spectra could be destroyed by throwing a book of data at it, so complex were the spectra.) Following Einstein’s proposal of photons with quantized energies directly proportional to their wavelengths, it became even more evident that electrons in atoms can exist only in discrete orbits.
In some cases, it had been possible to devise formulas that described the emission spectra. As you might expect, the simplest atom -- hydrogen, with its single electron -- has a relatively simple spectrum. The hydrogen spectrum had been observed in the infrared (IR), visible, and ultraviolet (UV), and several series of spectral lines had been observed. (See Figure \(\PageIndex{3}\).) These series are named after early researchers who studied them in particular depth.
The observed hydrogen-spectrum wavelengths can be calculated using the following formula:
\[\frac{1}{\lambda} = R \left( \frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}} \right), \label{30.4.1}\]
where \(\lambda\) is the wavelength of the emitted EM radiation and \(R\) is the Rydberg constant, determined by the experiment to be
\[R = 1.097 \times 10^{7}/m \left( or m^{-1} \right).\label{30.4.2}\]
The constant \(n_{f}\) is a positive integer associated with a specific series. For the Lyman series, \(n_{f} = 1\); for the Balmer series, \(n_{f} = 2\); for the Paschen series, \(n_{f} = 3\); and so on. The Lyman series is entirely in the UV, while part of the Balmer series is visible with the remainder UV. The Paschen series and all the rest are entirely IR. There are apparently an unlimited number of series, although they lie progressively farther into the infrared and become difficult to observe as \(n_{f}\) increases. The constant \(n_{i}\) is a positive integer, but it must be greater than \(n_{f}\). Thus, for the Balmer series, \( n_{f} = 2\) and \(n_{i} = 3, 4, 5, 6, \cdot \cdot \cdot\). Note that \(n_{i}\) can approach infinity. While the formula in the wavelengths equation was just a recipe designed to fit data and was not based on physical principles, it did imply a deeper meaning. Balmer first devised the formula for his series alone, and it was later found to describe all the other series by using different values of \(n_{f}\). Bohr was the first to comprehend the deeper meaning. Again, we see the interplay between experiment and theory in physics. Experimentally, the spectra were well established, an equation was found to fit the experimental data, but the theoretical foundation was missing.
Example \(\PageIndex{1}\): Calculating Wave Interference of a Hydrogen Line
What is the distance between the slits of a grating that produces a first-order maximum for the second Balmer line at an angle of \(15^{\circ}\)?
Strategy and Concept:
For an Integrated Concept problem, we must first identify the physical principles involved. In this example, we need to know (a) the wavelength of light as well as (b) conditions for an interference maximum for the pattern from a double slit. Part (a) deals with a topic of the present chapter, while part (b) considers the wave interference material of "Wave Optics."
Solution for (a):
Hydrogen spectrum wavelength. The Balmer series requires that \(n_{f} = 2\). The first line in the series is taken to be for \(n_{i} = 3\), and so the second would have \(n_{i} = 4\).
The calculation is a straightforward application of the wavelength equation. Entering the determined values for \(n_{f}\) and \(n_{i}\) yields
\[ \begin{align*} \frac{1}{\lambda} = R \left( \frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}} \right) \label{30.4.3} \\[5pt] &= \left(1.097 \times 10^{7} m^{-1}\right) \left( \frac{1}{2^{2}} - \frac{1}{4^{2}} \right) \\[5pt] &= 2.057 \times 10^{6} m^{-1}. \end{align*}\]
Discussion for (a):
This is indeed the experimentally observed wavelength, corresponding to the second (blue-green) line in the Balmer series. More impressive is the fact that the same simple recipe predicts all of the hydrogen spectrum lines, including new ones observed in subsequent experiments. What is nature telling us?
Solution for (b):
Double slit interference ("Wave Optics"). To obtain constructive interference for a double slit, the path length difference from two slits must be an integral multiple of the wavelength. This condition was expressed by the equation
\[d \sin{\theta} = m \lambda, \nonumber \]
where \(d\) is the distance between slits and \(\theta\) is the angle from the original direction of the beam. The number \(m\) is the order of the interference; \(m=1\) in this example. Solving for \(d\) and entering known values yields
\[d = \frac{\left(1\right) \left(486 nm\right)}{\sin{15^{\circ}}} = 1.88 \times 10^{-6} m. \nonumber\]
Discussion for (b):
This number is similar to those used in the interference examples of "Introduction to Quantum Physics" (and is close to the spacing between slits in commonly used diffraction glasses).
Bohr’s Solution for Hydrogen
Bohr was able to derive the formula for the hydrogen spectrum using basic physics, the planetary model of the atom, and some very important new proposals. His first proposal is that only certain orbits are allowed: we say that the orbits of electrons in atoms are quantized. Each orbit has a different energy, and electrons can move to a higher orbit by absorbing energy and drop to a lower orbit by emitting energy. If the orbits are quantized, the amount of energy absorbed or emitted is also quantized, producing discrete spectra. Photon absorption and emission are among the primary methods of transferring energy into and out of atoms. The energies of the photons are quantized, and their energy is explained as being equal to the change in energy of the electron when it moves from one orbit to another. In equation form, this is
\[\Delta E = hf = E_{i} - E_{f}. \label{30.4.5}\]
Here, \(\Delta E\) is the change in energy between the initial and final orbits, and \(hf\) is the energy of the absorbed or emitted photon. It is quite logical (that is, expected from our everyday experience) that energy is involved in changing orbits. A blast of energy is required for the space shuttle, for example, to climb to a higher orbit. What is not expected is that atomic orbits should be quantized. This is not observed for satellites or planets, which can have any orbit given the proper energy. (See Figure \(\PageIndex{4}\).)
Figure \(\PageIndex{5}\). shows an energy-level diagram , a convenient way to display energy states. In the present discussion, we take these to be the allowed energy levels of the electron. Energy is plotted vertically with the lowest or ground state at the bottom and with excited states above. Given the energies of the lines in an atomic spectrum, it is possible (although sometimes very difficult) to determine the energy levels of an atom. Energy-level diagrams are used for many systems, including molecules and nuclei. A theory of the atom or any other system must predict its energies based on the physics of the system.
Bohr was clever enough to find a way to calculate the electron orbital energies in hydrogen. This was an important first step that has been improved upon, but it is well worth repeating here, because it does correctly describe many characteristics of hydrogen. Assuming circular orbits, Bohr proposed that the angular momentum \(L\) of an electron in its orbit is quantized , that is, it has only specific, discrete values. The value for \(L\) is given by the formula \[L = m_{e}vr_{n} = n\frac{h}{2\pi} \left(n = 1,2,3, \cdot \cdot \cdot \right), \label{30.4.6}\] where \(L\) is the angular momentum, \(m_{e}\) is the electron’s mass, \(r_{n}\) is the radius of the \(n\)the orbit, and \(h\) is Planck’s constant. Note that angular momentum is \[L = I \omega. \label{30.4.7}\] For a small object at a radius \(r\), \[I = mr^{2}\label{30.4.8}\] and \[\omega = \frac{v}{r}\label{30.4.9}\], so that \[L = \left(mr^{2}\right)\left(\frac{v}{r}\right) = mvr. \label{30.4.10}\] Quantization says that this value of \(mvr\) can only be equal to \(h/2, 2h/2, 3h/2\), etc. At the time, Bohr himself did not know why angular momentum should be quantized, but using this assumption he was able to calculate the energies in the hydrogen spectrum, something no one else had done at the time.
From Bohr’s assumptions, we will now derive a number of important properties of the hydrogen atom from the classical physics we have covered in the text. We start by noting the centripetal force causing the electron to follow a circular path is supplied by the Coulomb force. To be more general, we note that this analysis is valid for any single-electron atom. So, if a nucleus has \(Z\) protons (\(Z = 1\) for hydrogen, 2 for helium, etc.) and only one electron, that atom is called a hydrogen-like atom . The spectra of hydrogen-like ions are similar to hydrogen, but shifted to higher energy by the greater attractive force between the electron and nucleus. The magnitude of the centripetal force is \(m_e v^2/r_n\), while the Coulomb force is \(k(Zq_e)(q_e)/r_n^2\). The tacit assumption here is that the nucleus is more massive than the stationary electron, and the electron orbits about it. This is consistent with the planetary model of the atom. Equating these,
\[k\dfrac{Zq_e^2}{r_n^2} = \dfrac{m_e v^2}{r_n} (Coulomb = centripetal).\]
Angular momentum quantization is stated in an earlier equation. We solve that equation for \(v\), substitute it into the above, and rearrange the expression to obtain the radius of the orbit. This yields: \[r_n = \dfrac{n^2}{Z} a_B, \, for \, allowed \, orbits \, (n = 1, \, 2, \, 3, . . . ),\]
where \(a_B\) is defined to be the Bohr radius , since for the lowest orbit (\( n = 1 \)) and for hydrogen \((Z = 1)\), \(r_1 = a_B\). It is left for this chapter’s Problems and Exercises to show that the Bohr radius is
\[a_B = \dfrac{h^2}{4 \pi^2 m_e kq_e^2} = 0.529 \times 10^{-10} \, m.\]
These last two equations can be used to calculate the radii of the allowed (quantized) electron orbits in any hydrogen-like atom . It is impressive that the formula gives the correct size of hydrogen, which is measured experimentally to be very close to the Bohr radius. The earlier equation also tells us that the orbital radius is proportional to \(n^2\), as illustrated in Figure \(\PageIndex{6}\).
To get the electron orbital energies, we start by noting that the electron energy is the sum of its kinetic and potential energy: \[ E_n = KE + PE.\] Kinetic energy is the familiar \(KE = (1/2)m_e v^2\), assuming the electron is not moving at relativistic speeds. Potential energy for the electron is electrical, or \(PE = q_e V\), where \(V\) is the potential due to the nucleus, which looks like a point charge. The nucleus has a positive charge \(Zq_e\); thus \(V = kZq_e/r_n\), recalling an earlier equation for the potential due to a point charge. Since the electron’s charge is negative, we see that \(PE = -kZq_e/r_n\). Entering the expressions for \(KE\) and \(PE\), we find \[E_n = \dfrac{1}{2} m_ev^2 - k\dfrac{Zq_e^2}{r_n}.\]
Now we substitute \(r_n\) and \(v\) from earlier equations into the above expression for energy. Algebraic manipulation yields \[E_n = \dfrac{Z^2}{n^2} E_0(n = 1, \, 2, \, 3, ...)\]
for the orbital energies of hydrogen-like atoms . Here, \(E_0\) is the ground-state energy (\(n = 1)\) for hydrogen \((Z = 1)\) and is given by
\[E_0 = \dfrac{2 \pi^2 Q_e^4 m_e k^2}{h^2} = 13.6 \, eV.\]
Thus, for hydrogen,
\[E_n = - \dfrac{13.6 \, eV}{n^2} (n = 1, \, 2, \, 3, ...).\]
Figure \(\PageIndex{7}\) shows an energy-level diagram for hydrogen that also illustrates how the various spectral series for hydrogen are related to transitions between energy levels.
Electron total energies are negative, since the electron is bound to the nucleus, analogous to being in a hole without enough kinetic energy to escape. As \(n\) approaches infinity, the total energy becomes zero. This corresponds to a free electron with no kinetic energy, since \(r_N\) gets very large for large \(n\), and the electric potential energy thus becomes zero. Thus, 13.6 eV is needed to ionize hydrogen (to go from –13.6 eV to 0, or unbound), an experimentally verified number. Given more energy, the electron becomes unbound with some kinetic energy. For example, giving 15.0 eV to an electron in the ground state of hydrogen strips it from the atom and leaves it with 1.4 eV of kinetic energy.
Finally, let us consider the energy of a photon emitted in a downward transition, given by the equation to be \[\Delta E = hf = E_i - E_f.\] Substituting \(E_n = (-13.6 \, eV/n^2)\), we see that \[hf = (13.6 \, eV)\left(\dfrac{1}{n_f^2} - \dfrac{1}{n_i^2}\right).\]
Dividing both sides of this equation by \(hc\) gives an expression for \(1/\lambda\):
\[\dfrac{hf}{hc} = \dfrac{f}{c} = \dfrac{1}{\lambda} = \dfrac{(13.6 \, eV)}{hc} \left(\dfrac{1}{n_f^2} - \dfrac{1}{n_i^2}\right).\] It can be shown that \[\left(\dfrac{13.6 \, eV}{hc} \right) = \dfrac{(13.6 \, eV)(1.602 \times 10^{-19} \, J/eV)}{(6.626 \, 10^{-34} \, J \cdot s)(2.998 \times 10^8 \, m/s)} = 1.097 \times 10^7 \, m^{-1} = R\] is the Rydberg constant . Thus, we have used Bohr’s assumptions to derive the formula first proposed by Balmer years earlier as a recipe to fit experimental data. \[\dfrac{1}{\lambda} = R \left(\dfrac{1}{n_f^2} - \dfrac{1}{n_i^2} \right)\]
We see that Bohr’s theory of the hydrogen atom answers the question as to why this previously known formula describes the hydrogen spectrum. It is because the energy levels are proportional to \(1/n^2\), where \(n\) is a non-negative integer. A downward transition releases energy, and so \(n_i\) must be greater than \(n_f\). The various series are those where the transitions end on a certain level. For the Lyman series, \(n_f = 1\) that is, all the transitions end in the ground state (see also Figure ). For the Balmer series, \(n_f = 2\), or all the transitions end in the first excited state; and so on. What was once a recipe is now based in physics, and something new is emerging—angular momentum is quantized.
Triumphs and Limits of the Bohr Theory
Bohr did what no one had been able to do before. Not only did he explain the spectrum of hydrogen, he correctly calculated the size of the atom from basic physics. Some of his ideas are broadly applicable. Electron orbital energies are quantized in all atoms and molecules. Angular momentum is quantized. The electrons do not spiral into the nucleus, as expected classically (accelerated charges radiate, so that the electron orbits classically would decay quickly, and the electrons would sit on the nucleus—matter would collapse). These are major triumphs.
But there are limits to Bohr’s theory. It cannot be applied to multielectron atoms, even one as simple as a two-electron helium atom. Bohr’s model is what we call semiclassical . The orbits are quantized (nonclassical) but are assumed to be simple circular paths (classical). As quantum mechanics was developed, it became clear that there are no well-defined orbits; rather, there are clouds of probability. Bohr’s theory also did not explain that some spectral lines are doublets (split into two) when examined closely. We shall examine many of these aspects of quantum mechanics in more detail, but it should be kept in mind that Bohr did not fail. Rather, he made very important steps along the path to greater knowledge and laid the foundation for all of atomic physics that has since evolved.
PHET EXPLORATIONS: MODELS OF THE HYDROGEN ATOM
How did scientists figure out the structure of atoms without looking at them? Try out different models by shooting light at the atom. Check how the prediction of the model matches the experimental results.
Figure \(\PageIndex{8}\): Models of the Hydrogen Atom
Summary
- The planetary model of the atom pictures electrons orbiting the nucleus in the way that planets orbit the sun. Bohr used the planetary model to develop the first reasonable theory of hydrogen, the simplest atom. Atomic and molecular spectra are quantized, with hydrogen spectrum wavelengths given by the formula \[\dfrac{1}{\lambda} = R\left(\dfrac{1}{n_f^2} - \dfrac{1}{n_i^2}\right), \nonumber\] where \(\lambda\) is the wavelength of the emitted EM radiation and \(R\) is the Rydberg constant, which has the value \[R = 1.097 \times 10^7 \, m^{-1}. \nonumber\]
- The constants \(n_i\) and \(n_f\) are positive integers, and \(n_i\) must be greater than \(n_f\).
- Bohr correctly proposed that the energy and radii of the orbits of electrons in atoms are quantized, with energy for transitions between orbits given by \[\Delta E = hf = E_i - E_f,\] where \(\Delta E\) is the change in energy between the initial and final orbits and \(hf\) is the energy of an absorbed or emitted photon. It is useful to plot orbital energies on a vertical graph called an energy-level diagram.
- Bohr proposed that the allowed orbits are circular and must have quantized orbital angular momentum given by \[L = m_evr_n = n\dfrac{h}{2\pi} (n = 1, \, 2, \, 3, . . .), \nonumber\] where \(L\) is the angular momentum, \(r_n\) is the radius of the \(n\)th orbit, and \(h\) is Planck’s constant. For all one-electron (hydrogen-like) atoms, the radius of an orbit is given by \[r_n = \dfrac{n^2}{Z}a_B(allowed \, orbits \, n = 1, \, 2, \, 3, ...), \nonumber\] \(Z\) is the atomic number of an element (the number of electrons is has when neutral) and \(a_B\) is defined to be the Bohr radius, which is \[a_B = \dfrac{h^2}{4 \pi^2m_ekq_e^2} = 0.529 \times 10^{-10} \, m. \nonumber\]
- Furthermore, the energies of hydrogen-like atoms are given by \[E_n = - \dfrac{Z^2}{n^2}E_0 (n = 1, \, 2, \, 3 ... ), \nonumber\] where \(E_0\) is the ground-state energy and is given by \[E_0 = \dfrac{2 \pi^2 q_e^4m_ek^2}{h^2} = 13.6 \, eV. \nonumber\] Thus, for hydrogen, \[E_n = - \dfrac{13.6 \, eV}{n^2} (n = 1, \, 2, \, 3, . . .). \nonumber\]
- The Bohr Theory gives accurate values for the energy levels in hydrogen-like atoms, but it has been improved upon in several respects.
Glossary
- hydrogen spectrum wavelengths
- the wavelengths of visible light from hydrogen; can be calculated by \(\frac{1}{\lambda} = R \left(\frac{1}{n_f^2} - \frac{1}{n_i^2} \right)\)
- Rydberg constant
- a physical constant related to the atomic spectra with an established value of \(1.097 \times 10^7 \, m^{-1}\)
- double-slit interference
- an experiment in which waves or particles from a single source impinge upon two slits so that the resulting interference pattern may be observed
- energy-level diagram
- a diagram used to analyze the energy level of electrons in the orbits of an atom
- Bohr radius
- the mean radius of the orbit of an electron around the nucleus of a hydrogen atom in its ground state
- hydrogen-like atom
- any atom with only a single electron
- energies of hydrogen-like atoms
- Bohr formula for energies of electron states in hydrogen-like atoms: \(E_n = - \frac{Z^2}{n^2} E_0 (n = 1, \, 2, \, 3, . . . )\)


7.9: The Present and Past Progressive Tense
The Present and Past Progressive Tense Video
Instructor Video: The Present and Past Progressive Tense
Structure
| Verb stem | Progressive aspect marker | Present tense | Past tense |
| खा, जा | रहा, रहे, रही | हूँ, हो, है, हैं | था, थे, थी, थीं |
| Example: |
|
|
Use of Progressive Aspect Marker with Different Subjects
Progressive markers (रहा, रहे, रही) are used based on the number, person and gender features of the agreeing subject.
| Person | Singular Pronoun |
Habitual markers
Masculine/Feminine |
Plural pronoun |
Habitual markers
Masculine/Feminine |
| 1st | मैं “I” | रहा/रही | हम “We” | रहे/रही |
| 2nd | तू “You” | रहा/रही | NA | |
| तुम “You” | रहे/रही | तुम (लोग) “You” | रहे/रही | |
| आप “You” | रहे/रही | आप (लोग) “You” | रहे/रही | |
| 3rd | यह/वह “S/he,” and singular noun | रहा/रही | ये/वे “They,” and plural nouns | रहे/रही |
Note: When subject of a sentence is of mixed gender please use plural masculine aspect marker.
Negation of Progressive Aspect
In order to change progressive aspect sentences in negative, we use the word नहीं right before the verb. When progressive sentences appear in negative, generally, the verb “to be” in present (हूँ, हो, है, हैं) are dropped, but not in the past (था, थे, थी, थीं). Negative of past tense keeps the past form of the verb “to be”
Examples:
- लड़कियां फुटबॉल खेल रही हैं | “Girls are playing football.”
- लड़कियां फुटबॉल नहीं खेल रहीं | “Girls are not playing football.”
- आप अपना कमरा साफ़ कर रहे थे | “You were cleaning your room.”
- आप अपना कमरा साफ़ नहीं कर रहे थे | “You were not cleaning your room.”
Note: Please notice the extra nasal dot “रहीं” in negative sentences with subject लड़कियां “girls.” As we drop the verb “to be,” the dot indicates the plural feminine subject in contrast to singular feminine subject.
Uses of Progressive Aspect
(a) To express action happening at the time of speaking.
Examples:
- बारिश हो रही है | “It is raining.”
- सब लोग सो रहे हैं | “Everyone is sleeping.”
- सीता और गीता एक फ़िल्म देख रही थीं | “Sita and Geeta were watching a film.”
Activity:
Please add five more examples here. After writing your examples please change your sentences in negative and past tense.
| Examples | Negative | Past tense | |
| 1. | |||
| 2. | |||
| 3. | |||
| 4. | |||
| 5. |
(b) To express temporary action. Generally, adverbs like, आजकल “these days,” and अभी “right now” are used.
Examples:
- सीता अभी किताब पढ़ रही है | “Sita is reading a book right now.”
- राहुल आजकल गिटार बजा रहा है | “Rahul is playing a guitar these days.”
- ऋतिक अमेरिका में रह रहा था | “Hrithik was living/staying in America.”
Activity:
Please add five more examples here. After writing your examples please change your sentences in negative and past tense.
| Examples | Negative | Past tense | |
| 1. | |||
| 2. | |||
| 3. | |||
| 4. | |||
| 5. |
(c) To express planned future action. The sentences must have future adverbs of time.
Examples:
- पीटर अगले महीने हिन्दुस्तान जा रहा है | “Peter is going to India next month.”
- जेन कल काम कर रही है | “Jen is working tomorrow.”
- मैं अगले हफ़्ते एक फ़िल्म देख रही हूँ | “I am watching a film next week.”
Note: To express planned future action using progressive aspect is only possible in present tense. Past tense of progressive aspect cannot express planned future action.
Activity:
Please add five more examples here. After writing your examples please change your sentences in negative and past tense.
| Examples | Negative | Past tense | |
| 1. | |||
| 2. | |||
| 3. | |||
| 4. | |||
| 5. |
Activities
(a) Please choose the correct progressive aspect markers based on the subject of the sentence.
https://openbooks.lib.msu.edu/ll151/?p=1110
(b) Please write 5 sentences explaining what you were doing last weekend.
| 1. | पिछले सप्ताहांत, मैं ________________________________________________________________________ था/थी | |
| 2. | |
| 3. | |
| 4. | |
| 5. |
(c) Please write 5 sentences explaining what you are doing next weekend.
| 1. | अगले सप्ताहांत, मैं ________________________________________________________________________ हूँ | |
| 2. | |
| 3. | |
| 4. | |
| 5. |
धन्यवाद !


1: Prerequisites
In this chapter, we will review sets of numbers and properties of operations used to manipulate numbers. This understanding will serve as prerequisite knowledge throughout our study of algebra and trigonometry.
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- 1.2: Real Numbers - Algebra Essentials
- It is often said that mathematics is the language of science. If this is true, then the language of mathematics is numbers. The earliest use of numbers occurred 100 centuries ago in the Middle East to count, or enumerate items. Because of the evolution of number systems, we can now perform complex calculations using these and other categories of real numbers. In this section, we will explore sets of numbers, calculations with different kinds of numbers, and the use of numbers in expressions.
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- 1.6: Factoring Polynomials
- The greatest common factor, or GCF, can be factored out of a polynomial. Checking for a GCF should be the first step in any factoring problem. Trinomials with leading coefficient 1 can be factored by finding numbers that have a product of the third term and a sum of the second term. Trinomials can be factored using a process called factoring by grouping. Perfect square trinomials and the difference of squares are special products and can be factored using equations.
Thumbnail: A shortcut called FOIL is sometimes used to find the product of two binomials. It is called FOIL because we multiply the first terms, the outer terms, the inner terms, and then the last terms of each binomial.
Contributors
- Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (formerly of Santa Ana College). This content produced by OpenStax and is licensed under a Creative Commons Attribution License 4.0 license.


1.2: Reference- Blackboard Tutorials
Below is a list of tutorials for using some of the student tools and features in Blackboard Learn 9.1 SP 14. (Note all links open in new window.)
Navigating a Blackboard Course
Announcements
Assignments
Discussion Board
- Discussion Board Overview
- Viewing a Dicussion Board Forum
- Creating a Discussion Thread
- Replying to a Discussion Thread
- Managing Discussion Threads
Opening a File in Blackboard
- Opening and Saving a File in Blackboard (PDF opens in new window)
Taking Tests and Quizzes
Working in Groups
Blackboard Help
Blackboard Collaborate
- Getting Started for Participants Quick Reference Guide (PDF file download)
- Participant Orientation (video recording)


4.1: Introduction
Many couples envision starting a family without any issues and within the first few months of trying. The reality, though, is that conception is a complex process. The average success rate is only 20 percent to 37 percent for the average young, fertile, and healthy couple becoming pregnant in the first 3 months of trying (Practice Committee of the American Society for Reproductive Medicine, 2017). While most couples do eventually achieve a pregnancy, a small subset of patients requires medical intervention. Some people expect to need infertility treatment, such as those with known medical conditions, members of same-sex relationships, or people who chose to become single parents. Nurses can provide education, community referrals, and emotional support during this time.