# If an electron has a spin quantum no. of "+1/2" and a magnetic quantum no. of -1, it cannot be present in?

## (a) d-orbital (b) f-orbital (c) p-orbital (d) s-orbital

Apr 7, 2018

(d) $s$ orbital

#### Explanation:

The trick here is to realize that an $s$ orbital cannot be described by a magnetic quantum number equal to $- 1$.

The $s$ subshell contains a single $s$ orbital, which implies that the magnetic quantum number, which tells you the orientation of the orbital that holds a given electron, can only take $1$ possible value.

More specifically, for an $s$ subshell, you have

$l = 0$

The angular momentum quantum number, $l$, describes the energy subshell in which the electron resides.

For a given subshell, the relationship between the angular momentum quantum number and the magnetic quantum number is given by

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

This means that for the $s$ subshell, you have

${m}_{l} = 0$

as the only value that the magnetic quantum number can take.

Consequently, you can say that

${m}_{l} = - 1$

cannot describe an electron located in an $s$ orbital because an $s$ orbital can only be described by ${m}_{l} = 0$.