Question

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

l = 3
m = 3
l = 0
m = –2
l = –1
m = 2

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
`+(1)/(2)` for upward spin and
`-(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=+(1)/(2)\text{ and }-(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`