# Question #254fb

Apr 25, 2017

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

$n = 3 \mathmr{and} {m}_{l} = - 2$

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

$l = \left\{0 , 1 , 2\right\}$

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

$n = 3 \mathmr{and} {m}_{l} = - 2 \to \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{max 2 e}}^{-}}}}$

For the second set, you have

$n = 5 \mathmr{and} l = 0$

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 $l = 0$

${m}_{l} = 0 \to$ 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

$n = 5 \mathmr{and} l = 0 \to \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{max 2 e}}^{-}}}}$

Finally, you have

$n = 4 , l = 3 , \mathmr{and} {m}_{l} = - 1$

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

$n = 5 , l = 3 , \mathmr{and} {m}_{l} = - 1 \to \textcolor{\mathrm{da} r k g r e e n}{\underline{\textcolor{b l a c k}{{\text{max 2 e}}^{-}}}}$