申論題

3.(10%) One of the most famous theories of the hydrogen atom was proposed by Bohr. It has been replaced by quantum mechanics but, by a remarkable coincidence, the energies it predicts agree exactly with those obtained from the Schrödinger equation. In the Bohr atom, an electron travels in a circle around the nucleus. The Coulombic force of Ze² attraction (), where Z is the atomic number is balanced by the centrifugal effect of the orbital motion. Bohr proposed that the angular momentum is limited to integral values of h. When the two forces are balanced, the atom remains in a stationary state until it makes a spectral transition. Instead of using this approach, we applied the standing wave condition for the de Broglie wave associated with the electron in class. Now you are asked to follow our approach to solve the following two problems:

(b) (3%) Calculate the allowed energies of a hydrogenic atom using the hybrid Bohr-de Broglie model.