Question

For the n = 3 electron shell, which of the following quantum numbers are valid? Check all that apply.

Answer 1

Since l can be 0,1,2... up to n-1 and m can be -l, -l+1... up to l, I say this

l=0, m=2, m=-2. It's worth saying that these equalities can not be simultaneous, but they are possible for the shell n=3 separately

Answer 2

Answer : The correct options are, $l=0,m=-2\text{ and }m=2$

Explanation :

Principle Quantum Numbers : It describes the size of the orbital and the energy level. It is represented by n. Where, n = 1,2,3,4....

Azimuthal Quantum Number : It describes the shape of the orbital. It is represented as 'l'. The value of l ranges from 0 to (n-1). For l = 0,1,2,3... the orbitals are s, p, d, f...

Magnetic Quantum Number : It describes the orientation of the orbitals. It is represented as $m_l$. The value of this quantum number ranges from $(-l\text{ to }+l)$. When l = 2, the value of $m_l$ will be -2, -1, 0, +1, +2.

Spin Quantum number : It describes the direction of electron spin. This is represented as $m_s$ The value of this is $+\frac{1}{2}$ for upward spin and $-\frac{1}{2}$ for downward spin.

As we are given that,  $n=3$

So,

$l=0,1,2$

$m_l=-2,-1,0,1,2$

$m_s=+\frac{1}{2}\text{ and }-\frac{1}{2}$ (For each sub-shell)

Hence, from this we conclude that, the valid quantum numbers are $l=0,m=-2\text{ and }m=2$