Draw the electron configuration diagram for carbon?

Each row on 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