# Question #930df

Feb 3, 2018

$n - 1$

#### Explanation:

The orbital quantum number, which is usually called the angular momentum quantum number, $l$, depends on the value of the principal quantum number, $n$.

In other words, the number of values that the angular momentum quantum number, which denotes the energy subshell in which an electron is located inside an atom, i.e. the sphape of the orbital(s), can take is limited by the value of the principal quantum number, which denotes the energy shell in which the electron is located.

For a given energy shell $n$, you will have

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

As you can see, the number of values that the angular momentum quantum number can take is equal to $n$, but the maximum value that this quantum number can take is equal to $n - 1$.

For example, the third energy shell, which is denoted by $n = 3$, can hold $3$ energy subshell because the angular momentum quantum number can take $3$ values.

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

Notice that in this case, the maximum value that the angular momentum quantum number can take is $2$, since

$3 - 1 = 2$