Kinetic isotope effect approximation that reduced masses are approximately equal to the masses of the hydrogen, deuterium, or tritium was used. In addition, the vibrational motion was assumed to be approximated by a harmonic oscillator, so that formula_19 (X = H, D, or T). The subscript ""s"" refers to these "semi-classical" kinetic isotope effects, which disregard quantum tunneling. Tunneling contributions must be treated separately as a correction factor. For isotope effects involving elements other than hydrogen, many of these simplifications are not valid, and the magnitude of the isotope effect may depend strongly on some or all of the neglected factors. Thus, kinetic
Isotope 40 different species referred to as "radioelements" (i.e. radioactive elements) between uranium and lead, although the periodic table only allowed for 11 elements from uranium to lead. Several attempts to separate these new radioelements chemically had failed. For example, Soddy had shown in 1910 that mesothorium (later shown to be Ra), radium (Ra, the longest-lived isotope), and thorium X (Ra) are impossible to separate. Attempts to place the radioelements in the periodic table led Soddy and Kazimierz Fajans independently to propose their radioactive displacement law in 1913, to the effect that alpha decay produced an element two places to the