Quantum physics underlining the 'magic numbers' in chemical bonding & more.

[bentzy]

a. What do we know about any quantum-physical law, dictating 8 electrons in the outer atomic shell + the other shells' populations, including the 2 electrons in the innermost. Any physical theory behind these numbers, or just an empirical reality ?

b. How reacting atoms 'choose' between, e.g., ionic bond and covalent bond ?

c. What Hydrogen was used in the early spectra measurements (e.g., Balmer) - atomic or molecular ? Since the spectra are atomic in nature, how did they split the H molecule into two atoms in those days ?

 

[Wolfgang2b]

Let me take a try at the question (a)

The number of electrons in the shell come from "quantum numbers". While solving the Schrödinger equation for Hydrogen atom, we get 3 quantum numbers : n (principal), l (orbital) and ml (magnetic). The values these take are given as

n : 1,2,3,,,, (This number refers to "shells")
l : 0 to n-1
ml: -l to l

All of these are integers.

Apart from this we have a quantum number for spin(ms), which takes only 2 values.

The combination of all the 4 quantum numbers define a quantum state (n,l,ml,ms). As per Pauli's exclusion principle, each of these states can be occupied by only one electron.

So if you start from n=1, and apply the above rules, you will see that for n=1, l = 0, and ml =0. So we have only one combination. But we have 2 values for ms. So that means, we have 2 quantum states for n=1. Hence the lowermost shell, can take 2 electrons.

From this, you can continue for n=2 etc...