How many electrons fit in a shell?

The idea

The maximum number of electrons in a shell is 2n², where n is the shell number, so the K, L and M shells can hold 2, 8 and 18 electrons.

Seats in each shell

Each shell is like a row of seats around the nucleus. The farther the row, the more seats it has.

The K shell holds 2 electrons. How many do you think the L shell (the next shell) holds?

• 8
• 3
• 4

Seats in the shell

Change the shell number n and watch the number of electrons the shell can hold.

The 2n² rule

Bohr and Bury suggested a formula: the shell with number n can hold at most 2n² electrons. For n = 1, 2, 3 that gives 2, 8 and 18.

The maximum number of electrons in a shell is 2n², where n is the shell number. So the K, L and M shells can hold 2, 8 and 18 electrons.

Notes

The maximum number of electrons in a shell is 2n² (n is the shell number): K 2, L 8, M 18.

Check yourself

Using 2n², how many electrons can the M shell (n = 3) hold at most?

Answer: 18

2 × 3² = 2 × 9 = 18.

Using 2n², how many electrons can the L shell (n = 2) hold at most?

Answer: 8

2 × 2² = 2 × 4 = 8.

Which formula gives the maximum number of electrons in the shell with number n?

Using the same formula, how many electrons can the N shell (n = 4) hold at most?

Answer: 32

2 × 4² = 2 × 16 = 32.

• 2n² — correct. Yes!
• 2n. For n = 2 this gives 4, but the L shell can hold 8.
• n². For n = 1 this gives 1, but the K shell can hold 2.