Question

If a shell contains a maximum of 32 electrons, what is the principal quantum number,n?

Short answer

The value of $n=4$.

Step-by-step solution

The maximum number of electrons in a shell

The maximum number of electrons in a shell can be calculated by using the formula$\mathbf{2}{\mathbf{n}}^{\mathbf{2}}$.

By using this formula, the “n” value can be determined.

The value of “n”

The maximum number of electrons in the given shell are 32.

The maximum number of electrons in a shell are$2n^2$.

Hence,

$\begin{array}{r}2n^2=32\\ n^2=16\\ n=\sqrt{16}\\ n=4\end{array}$

Thus, the value of “n” is four.