Question

Question #254fb

Answer 1

Here's what I got.

Explanation:

As you know, we can use four quantum numbers to describe the position and the spin of an electron in an atom.

For the first set, you have

`n =3 and m_l = -2`

The principal quantum number, `n`, tells you the energy level, or energy shell, on which the electron resides.

The energy shell determines the energy subshell, which is given by the angular momentum quantum number, `l`.

In this case, you have

`l = {0, 1, 2}`

The magnetic quantum number, `m_l`, tells you the orbital in which the electron is located. As you can see on the table, `m_l` depends on `l`.

More specifically, `m_l = -2` is one of the five orbitals available for

`l = 2`

which describes the `d` subshell.

Now, every orbital can hold a maximum of `2` electrons of opposite spins, as given by the Pauli Exclusion Principle. This means that a maximum of `2` electrons can share

`n = 3 and m_l = -2 -> color(darkgreen)(ul(color(black)("max 2 e"^(-))))`

For the second set, you have

`n = 5 and l= 0`

This time, you have the fifth energy level and the `s` subshell. As you can see, the magnetic quantum number can only take one value for `l=0`

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

Once again, you are dealing with a single orbital, which means that you will have a maximum of `2` electrons that can share

`n = 5 and l = 0 -> color(darkgreen)(ul(color(black)("max 2 e"^(-))))`

Finally, you have

`n=4, l=3, and m_l = -1`

This time, you are working on the fourth energy level, in the `f` subshell, which is described by `l=3`.

Once again, the fact that you have a single value for `m_l` tells you that you are working with a single orbital, which means that you will have a maximum of `2` electrons that can share

`n=5, l=3, and m_l = -1 -> color(darkgreen)(ul(color(black)("max 2 e"^(-))))`