Question

Draw the electron configuration diagram for carbon?

Answer 1

Each row on the periodic table introduces a new value for the principal quantum number `n`, while `l` goes as `0, 1, . . . , n-1`.

Recall that `l = 0 -> s` orbital, and `l = 1 -> p` orbital. Therefore, we would have these orbitals available:

`"Row 1:"` `1s`
`"Row 2:"` `2s, 2p`
`"Row 3:"` `. . .`
`"Row 4:"` `. . .`

Carbon has access to only `n = 2` and `n = 1`, so its six electrons can only go into the `1s`, `2s` and `2p` orbitals, from lowest to highest energy (Aufbau Principle) one at a time to maximize spin (Hund's Rule), with opposite spins when pairing up (Pauli Exclusion Principle).

`1s^2 2s^2 2p^2`:

`color(white)([(color(black)(ul(uarr color(white)(darr)))),(color(black)(2p_x))]) color(white)([(color(black)(ul(uarr color(white)(darr)))),(color(black)(2p_y))]) color(white)([(color(black)(ul(color(white)(darr) color(white)(darr)))),(color(black)(2p_z))])`

`color(white)([(color(black)(ul(uarr darr))),(color(black)(2s))])`

`" "`
`" "`

`color(white)([(color(black)(ul(uarr darr))),(color(black)(1s))])`

If you want to read more on it:
https://socratic.org/questions/how-do-you-draw-electron-orbital-diagrams