Question

How many electrons will fit in (show math)
energy level 1


energy level 2


energy level 3


energy level 4

Answer 1

The number of electrons that can occupy a given energy level (or shell) in an atom can be determined using the formula:

\[
N = 2n^2
\]

where \( N \) is the maximum number of electrons, and \( n \) is the principal quantum number corresponding to the energy level.

Let's calculate the number of electrons for each energy level:

### Energy Level 1 (n = 1)
\[
N = 2(1^2) = 2(1) = 2
\]

### Energy Level 2 (n = 2)
\[
N = 2(2^2) = 2(4) = 8
\]

### Energy Level 3 (n = 3)
\[
N = 2(3^2) = 2(9) = 18
\]

### Energy Level 4 (n = 4)
\[
N = 2(4^2) = 2(16) = 32
\]

### Summary of Results

- **Energy Level 1**: 2 electrons
- **Energy Level 2**: 8 electrons
- **Energy Level 3**: 18 electrons
- **Energy Level 4**: 32 electrons

Thus, the maximum number of electrons that can fit in each of the first four energy levels is 2, 8, 18, and 32 respectively.