# 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?

Jun 29, 2017

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

$2 l + 1 = 2 \cdot 4 + 1 = \text{9 orbitals}$,

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

$= 9 \cdot 2 = 18$ ${e}^{-}$

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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

$l = 0 , 1 , 2 , 3 ,$

${m}_{l} \text{ for " l = 3} = \left\{- 3 , - 2 , - 1 , 0 , 1 , 2 , 3\right\}$

${m}_{l} \text{ for " l = 2} = \left\{- 2 , - 1 , 0 , 1 , 2\right\}$

${m}_{l} \text{ for " l = 1} = \left\{- 1 , 0 , 1\right\}$

${m}_{l} \text{ for " l = 0} = \left\{0\right\}$