Question

What is the maximum number of electrons that can occupy the `l = 4` subshell? What are the possible sets of 4 quantum numbers for an electron in `n = 4` orbitals?

Answer 1

The angular momentum quantum number refers to the type of orbital and it can have multiple values for a single energy level.

Its value can be determined from magnetic quantum number and principal quantum number.

`l = 0, 1, . . . , n-1`

Therefore in this case the energy level can be `n = 5` or higher, but we only concern ourselves with orbitals that are used in known elements, so `n = 5` is suitable.

Qusetion 1 What is the maximum number of electrons that can occupy a given subshell of `l = 4`?

Starting with the first problem

As `l` refers to the shape of an orbital, the shapes of the orbitals can be determined from `l` which are designated with different names

First you to need to know the number of orbitals in the g subshell. Knowing that the number of degenerate orbitals is

`2l +1 = 2*4 + 1 = "9 orbitals"`,

and as each orbital can hold 2 electrons, electrons in 9 orbitals

`= 9*2 = 18` `e^-`

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Question 2 What are possible quantum numbers for an electron at energy level four?

The possible quantum numbers for `n=4` are then

`l = 0,1,2,3,`

`m_l " for " l = 3" = {-3,-2,-1,0,1,2,3}`

`m_l " for " l = 2" = {-2,-1,0,1,2}`

`m_l " for " l = 1" = {-1,0,1}`

`m_l " for " l = 0" = {0}`