# For the atomic shell with quantum number n = 1, how many sub-shells are possible where each sub-shell has a different value of the angular momentum quantum?

Nov 25, 2017

For n = 1 there is only one sub-shell => l = s = 0 & m = 0

#### Explanation:

Using the Aufbau Diagram and the 'building up sequence' of adding electrons into electronic orbitals; that is, electrons enter the lowest available energy level during the sequential building up the electronic cloud.

For a given Principle Quantum Number (n), the number of orbitals (or, suborbitals) associated with that energy level equals the value of n. That is, for

n = 1 => 1 sublevel => 1s
n = 2 => 2 sublevels => 2s 2p
n = 3 => 3 sublevels => 3s 3p 3d
n = 4 => 4 sublevels => 4s 4p 4d 4f
n = 5 => 5 sublevels => 5s 5p 5d 5f (5g)
n = 6 => 6 sublevels => 6s 6p 6d (6f)
(6g) (6h)
n = 7 => 7 sublevels => 7s 7p (7d) (7f) (7g) (7h) (7i)*
undiscovered
number values s => 0 p => 1 d => 2 f = 3

For the Angular Momenum QN (or, Magnetic QN) => number of orientations per known sublevels...

s => 1 => $\textcolor{w h i t e}{\left(m\right) \left(m\right) \left(m\right) \left(m\right)} \left({s}_{0}\right)$
p => 3 => $\textcolor{w h i t e}{\left(\right) \left(\right) \left(\right) \left(\right) \left(\right)} \left({p}_{- 1}\right) \left({p}_{0}\right) \left({p}_{+ 1}\right)$
d => 5 => $\textcolor{w h i t e}{\left(\right) \left(\right)} \left({d}_{- 2}\right) \left({d}_{- 1}\right) \left({d}_{0}\right) \left({d}_{+ 1}\right) \left({d}_{+ 2}\right)$
f => 7 => $\left({f}_{- 3}\right) \left({f}_{- 2}\right) \left({f}_{- 1}\right) \left({f}_{0}\right) \left({f}_{+ 1}\right) \left({f}_{+ 2}\right) \left({f}_{+ 3}\right)$

Spin QN ...
(m_+1/2) => clockwise spin
(m_ -1/2) => counterclockwise spin

Order of filling is frequently illustrated as follows in the Aufbau Diagram ...

For the 4 quantum numbers $\left(n , l , m , {m}_{s}\right)$ for a single 3p electron...