Question

The $m$ value not possible for a double dumbbell shaped orbital
A. $0$
B. $ - 2$
C. $ + 3$
D. $ - 1$

Answer 1

Hint: Shape of the orbital is characteristic to the shell it belongs to. Dumbbell shaped orbitals are only available in the d shell. The possible values for magnetic quantum numbers range from positive to negative values for azimuthal quantum numbers.

Complete step by step answer:
Let us understand the terms used in the question.
Let us understand the naming of azimuthal quantum number.
For S orbital, $l = 0$
For p orbital $l = 1$
For d orbital $l = 2$
We know that double dumbbell shaped orbits are orbitals in the d shell.
So, for d shell we know, $l = 2$ .
So, the value of magnetic quantum number $m$ is a range given by
$ - l$ to $ + l$
So, for d orbital it will be,
$ - 2$ to $ + 2$
So, the possible values are
$ - 2, - 1,0, + 1, + 2$
Therefore, the $m$ value not possible for a double dumbbell shaped orbital is $ + 3$ .

So, the correct answer is Option C .

Additional information:
magnetic quantum number is the third on the list between spin and azimuthal quantum number. It will split the sub-shells (such as s,p,d,f) into individual orbitals and it will place the electron in one of the subshells. It defines the orientation in space of a given orbital of particular energy and shape.
The magnetic quantum number primarily tells us the number of orbitals and the orientation of orbitals in the given subshell. It is dependent on the orbital angular momentum quantum number, also known as the azimuthal quantum number.

Note: d orbital have many different shapes. They have five orbitals which are dumbbell shapes in different combinations. There is a dumbbell shaped orbital with a donut shape in the middle. However, there are five sub orbitals and five values of magnetic quantum number ranging from $ - 2$ to $ + 2$ .