Atomic radius and electrons because opposite charges attract, and more protons creates a stronger charge. The greater attraction draws the electrons closer to the protons, decreasing the size of the particle. Therefore, atomic radius decreases. Down the groups, atomic radius increases. This is because there are more energy levels and therefore a greater distance between protons and electrons. In addition, electron shielding causes attraction to decrease, so remaining electrons can go farther away from the positively charged nucleus. Therefore, size (atomic radius) increases. The following table summarizes the main phenomena that influence the atomic radius of an element: The electrons in the
Particle in a box not strictly hold for the measured momentum ; the energy eigenstate formula_38 is not a momentum eigenstate, and, in fact, not even a superposition of two momentum eigenstates, as one might be tempted to imagine from equation () above: peculiarly, it has no well-defined momentum before measurement! In classical physics, the particle can be detected anywhere in the box with equal probability. In quantum mechanics, however, the probability density for finding a particle at a given position is derived from the wavefunction as formula_39 For the particle in a box, the probability density for finding the particle at a given