Question

What are the possible values of quantum number ℓ when n =1 ?

Answer 1

`l=0`

Explanation:

The relationship between the possible values of the angular momentum quantum number, `l`, and the principal quantum number, `n`, is given by

`color(blue)(ul(color(black)(l = {0, 1, 2, ..., n-1})))`

For a given quantum number `n`, the angular momentum quantum number can take `n` possible values that range from `0` to `n-1`.

In your case, you have `n=1`, which means that the angular momentum quantum number can take `1` possible value.

`l = 0`

This tells you that the first energy shell can hold a single energy subshell, the `s` subshell.

`n = 1, l= 0`

The electron is located in the first energy shell, in the `1s` subshell.

Consequently, the first energy shell can hold a single orbital, the `1s` orbital, because the magnetic quantum number, `m_l`, which tells you the number of distinct orbitals present in a given subshell, can take one possible value.

`m_l = {-1, - (l-1), ..., -1, 0, 1, ..., l-1, l}`

So for `l=0`, you have

`m_l = 0 ->` the `s` orbital

And so

`n =1, l= 0, m_l = 0`

The electron is located in the first energy level, in the `1s` subshell, and in the `1s` orbital.