Question

What do these sets of quantum numbers describe?

`a)` `(n,l,m_l,m_s) = (5,1,-1,+1/2)`
`b)` `(n,l,m_l,m_s) = (6,1,1,-1/2)`

Answer 1

As I'm sure you know, there are four quantum numbers used to describe the location of an electron.

In order, these four quantum numbers are

I'll start with the first one. The 5p subshell places your electron in one of the three 5p-orbitals, `5p_x`, `5p_y`, or `5p_z`. This means that a set of quantum numbers you can use has

`n=5` `->` the fifth energy level;
`l =1` `->` the 5p subshell;
`m_l=-1` `->` the `5p_x` orbital;
`m_s="+1/2"` `->` spin-up;

This set describes an electron that is located on the fifth energy level, in the 5p subshell, in the `5p_x` orbital and that has a spin-up.

Keep in mind, n = 5 and l = 1 are a must if you want your electron to be in the 5p subshell. You could however have other values for `m_l` (0 or +1) and `m_s` (-1/2).

Now for the second one. The 6p subshell has, once again, three 6p-orbitals: `6p_x`, `6p_y`, and `6p_z`. The same principle applies in this case as well

`n=6` `->` the sixth energy level;
`l =1` `->` the 6p subshell;
`m_l=+1` `->` the `6p_z` orbital;
`m_s="-1/2"` `->` spin-down;

This time, the numbers I've chosen describe an electron that is located on the sixth energy level, in the 6p subshell, in the `6p_z` orbital and that has spin-down.