# Question #c7b21

Oct 26, 2017

Here's what I got.

#### Explanation:

For starters, you know that the angular momentum quantum number, $l$, which gives you the energy subshell in which an electron is located in an atom, depends on the principal quantum number, $n$.

$l = \left\{0 , 1 , \ldots , n - 1\right\}$

$n = 3$

which implies

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

This tells you that the third energy level contains a total of $3$ energy subshells, each described by a value of the angular momentum quantum number.

Now, the magnetic quantum number, ${m}_{l}$, which tells you the specific orbital in which an electron is located, depends on the value of the angular momentum quantum number.

${m}_{l} = \left\{- l , - \left(l - 1\right) , \ldots , - 1 , 0 , 1 , \ldots , \left(l - 1\right) , l\right\}$

• $l = 0 \implies {m}_{l} = 0$

This tells you that $s$ subshell, which is denoted by $l = 0$, contains $1$ orbital.

• $l = 1 \implies \left\{\begin{matrix}{m}_{l} = - 1 \\ {m}_{l} = 0 \\ {m}_{l} = + 1\end{matrix}\right.$

This tells you that the $p$ subshell, which is denoted by $l = 1$, contains $3$ orbitals.

• $l = 2 \implies \left\{\begin{matrix}{m}_{l} = - 2 \\ {m}_{l} = - 1 \\ {m}_{l} = 0 \\ {m}_{l} = + 1 \\ {m}_{l} = + 2\end{matrix}\right.$

This tells you that the $d$ subshell, which is denoted by $l = 2$, contains $5$ orbitals.