Orbital 能量的問題。(40分!!!!!!)

Question

這個問題我想是化學的問題，但我認為這個問題應該是和quantum mechanics有關，應該在physics度問:
點解d電子有同一個principal quantum number n,但是都會有不同的能量?(如4s,4p,4d,4f orbital的能量不同)請詳細解答，我知是個l有分別，但是這個分別怎樣令到energy不同呢？

仲有，想問4s離nucleus遠d，還是3d? s,p,d,f,如果是同一個shell,邊個的volume最大?

Answer 1

This is a property of fermions.
Electrons belong to the class of fermions (the other class is Bosons, example of which is photons). Fermions obey the Pauli's Exclusion Principles which states that in a closed system of fermions (electrons), no two electrons shall possess the same quantum states (i.e. energy levels).

Apart from the principal quantum numbers which give the principal orbits of electrons (the K, L, M shells etc). Each of the principal orbit is sub-divided into sub-orbits, namely s, p, d, f, each of which are assigned an orbital angular momentum quantum number.

The s shell has 2 electrons, whereas the p shell has 6 electrons. The p shell actually composes of 3 sub-shells, given magnetic quantum numbers of -1, 0 and +1 to each sub-shell. Each of these sub-shells therefore accomodates 2 electrons. The two electrons have opposite spins, one is spin-up (rotating conunterclockwise) and the other spin-down (rotating clockwise) in order not to violate Pauli' Exclusion Principle.

Hence, each electrons in the p sub-orbit have a different set of quantum numbers and hence possess different energy levels.

Similar principle applies to other sub-orbits of d and f.

Therefore, in an atom, no two electrons possess the same energy levels. Pauli's Exlusion Principle must be followed.

Because of the mutual interaction between electrons, for elements with atomic number smaller than 40, the 3d orbital electrons have energy level lower than those at the 4s orbit. For heavy elements, 4s orbital electrons have higher energy than the 3d orbit electrons.