# What are the number of sub-levels and electrons for the first four principal quantum numbers?

Oct 23, 2015

For quantum number 1, the number of sub level is 1, number of electrons= 2.
For quantum number 2, no. of sub levels are 2, no. of electrons= 8. For quantum no. 3, sub levels are 3 and no. of electrons are 18.
For 4th quantum no. sub levels are 4 and electrons are 32.

#### Explanation:

You can easily calculate it with this method :

1. Suppose the principal quantum number is symbolized as $n$ the Azimuthal or secondary quantum number is symbolized as $l$
the magnetic Q.N is $m$
and the spin Q.N is $s$.

2. $n$ = which energy shell it is; $l$ = number of sub-shells; $m$ = number of orbitals as well as electrons.
$l$ =0, $n - 1$ and $m$ = $\pm$ l = $- l , 0 , + l$.

3. For example, in case of principal quantum number 2,
the result of $l$ is = $n - 1$ = 2-1 = 1, which means the number of subshells are two : 0 and 1.

Now the result for $m$ is : 0 = $s$ (one orbital of subshell $s$) = 2 electrons. And for 1 = -1, 0, +1 = ${P}_{x} , {P}_{y} \mathmr{and} {P}_{z}$ (3 orbitals of subshell $p$), electron = 6 ( each orbital can contain maximum 2 electrons ) .

So the total number of electrons for principal quantum number 2 is 8 .