Question

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

Answer 1

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` = `+-` 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 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 .