Question

The following combinations are not allowed. If n and ml are correct, change the l value to create an allowable combination:

Answer 1

The allowable combination for the atomic orbital is n=3, l=1, $m_{l}$=-1.

What are the three quantum numbers of an atomic orbital?

Three quantum numbers specify an atomic orbital:

- The principal quantum number, n, which is a positive integer, describes the relative size of the orbital and its distance from the nucleus.

- l is the angular momentum quantum number that is related to the shape of the orbital; l is an integer from 0 to n-1 (so n limits l ),

- $\boldsymbol{m}_{l}$ is the magnetic quantum number that prescribes the three-dimensional shape of the orbital around the nucleus; $m_{l}$ values are integers from -l to =l(l limits ml)

For n = 3, l can have three values: 0, 1, and 2. Since $m_{l}$ values are integers from -l to 0 to +l, for l = 0 the value of $m_{l}$ cannot be -1 (l = 0 has $m_{l}$= 0).

There are two l values that are consistent with n and $m_{l}$ values:

l=1 or 2

Therefore, the allowable condition is n=3, l=1, $m_{l}$=-1.

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