# How do you determine the number of electrons needed to fill the outer shell of an element?

Dec 25, 2017

$2 {n}^{2}$

#### Explanation:

The number of valence electrons needed to fill its shell can be determined by inputting the shell level, n, squaring it, and by multiplying by 2.

• Shell 1 holds 2 valence ${e}^{-}$.
$2 \left({1}^{2}\right) = 2$
• Shell 2 = 8
$2 \left({2}^{2}\right) = 8$
• Shell 3 = 18
$2 \left({3}^{2}\right) = 18$
• Shell 4 = 32
$2 \left({4}^{2}\right) = 32$
• Shell 5 = 50
$2 \left({5}^{2}\right) = 50$

You can decide whether you want to memorize the sequence in which each level can hold, "2, 8, 18, 32, 50, etc.," or you can remember this simple function of $2 {n}^{2}$ for a quick reference.