# Question #c7c7e

Oct 14, 2015

#### Explanation:

Once again, start by identifying which energy level, and implicitly principal quantum number, $n$, corresponds to the $N$ shell.

This time, you're dealing with the fourth energy level, $n = 4$.

You already know that the number of orbitals thatcan be found in each energy level is given by the equation

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

In your case, the fourth energy level will contain

$n = 4 \implies \text{no. of orbitals} = {4}^{2} = 16$

The number of subshells is given by the principal quantum number.

$\text{no. of subshells} = n$

In your case, the fourth energy level will have

$\text{no. of subshells} = 4$

subshells, each containing

• one 4s-orbital
• three 4p-orbitals
• five 4d-orbitals
• seven 4f-orbitals

Now, how about the number of electrons?

Well, each orbital can hold a maximum of two electrons, one having spin-up and one having spin-down.

This means that the maximum number of electrons a given shell, or energy level, can have is equal to

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

In your case, the fourth energy shell will can hold a maximum of

${\text{no. of electrons" = 2 * 4^2 = "32 e}}^{-}$

So, as a conclusion, all three options are corresct, which implies that the answer will be (d).