# Question #33d8c

##### 1 Answer
Oct 14, 2015

The answer is (c) $9$

#### Explanation:

Each electron shell corresponds to a different energy level, which is represented by the principal quantum number, $n$.

The $M$ shell designates the third energy level, for which $n = 3$.

The relationship between the principal quantum number and the number of orbitals is given by the equation

$\text{no. of orbitals} = {n}^{2}$

This equation will produce

$n = 1 \implies \text{no. of orbitals} = {1}^{2} = 1$

$n = 2 \implies \text{no. of orbitals} = {2}^{2} = 4$

$n = 3 \implies \text{no. of orbitals} = {3}^{2} = 9$

The $M$ shell will thus contain a total of $9$ orbitals

• one 3s-orbital
• three 3p-orbitals
• five 3d-orbitals