Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Richard777 on 08/12/2019 20:36:45

Title: Can Atomic number be expressed in terms of quantum numbers?
Post by: Richard777 on 08/12/2019 20:36:45
The four quantum numbers (n, L, mL, ms) are associated with an electron and are well defined in the literature.
A fifth quantum number (s) represents the spin momentum of an electron; s = ˝
Spin momentum is usually omitted because it has the same value for all leptons (including all electrons).

Atomic number represents the number of protons in the nucleus of an atom and may be used to represent any element. Each element may also designate a particular electron as a “most significant electron” (or most re-active electron).

Atomic number may be represented as the sum of two parts; one part is associated with electric charge and mass (momentum) and the other part includes magnetic moment. Each part may be related to the quantum numbers of the “most significant electron”.

Is it possible to calculate atomic number from the quantum numbers?
Title: Re: Can Atomic number be expressed in terms of quantum numbers?
Post by: Bored chemist on 08/12/2019 21:42:24
Is it possible to calculate atomic number from the quantum numbers?
No

It's not clear why you would want to but anyway,
You can have a hydrogen atom with essentially any (non forbidden) set of quantum numbers you want.
But the atomic number is still 1
On the other hand, if you count the electrons- whatever their quantum stare may be- you know the atomic number.
Title: Re: Can Atomic number be expressed in terms of quantum numbers?
Post by: Kryptid on 09/12/2019 01:14:32
Each element may also designate a particular electron as a “most significant electron” (or most re-active electron).

That actually wouldn't be the case for all (or may even most) elements. Take the two electrons in the 2s orbital of beryllium. Both have equal energy and are equally likely to participate in reactions.
Title: Re: Can Atomic number be expressed in terms of quantum numbers?
Post by: Bored chemist on 09/12/2019 07:20:11
Each element may also designate a particular electron as a “most significant electron” (or most re-active electron).
No it doesn't.
All electrons are equivalent.
"you can not paint an electron purple".
Title: Re: Can Atomic number be expressed in terms of quantum numbers?
Post by: evan_au on 09/12/2019 08:55:29
Quote from: OP
Is it possible to calculate atomic number from the quantum numbers?
The above discussion is talking about quantum numbers of electrons, which are only loosely related to the atomic number (especially if you include ions, where the number of electrons differs from the number of protons).

However, protons in the nucleus also have quantum numbers, including an arrangement in shells (which may be partially filled). Proton quantum numbers have a very direct relationship with the atomic number.
- Neutrons also come in shells, and have quantum numbers
- The energy levels of the proton and neutron shells are somewhat different, since the protons experience an electrostatic repulsion which does not affect neutrons.
- So, overall, the most stable nuclei have at least as many neutrons as protons .(once you get past Hydrogen)
See: https://en.wikipedia.org/wiki/Nuclear_shell_model