Question

If the quantum number l has a value of $2$, what are the permitted values of the quantum number m?
A.\[\; - 2, - 1,0,1,2\]
B.\[\;0,1,2,3,4\]
C.$0,1,2$
D.$ - 1,0,1$

Answer 1

Hint: In these kinds of questions related to quantum numbers, we just need the quantum number ‘n’, and from n we can easily find the other quantum number l and then from l we can find m. And m ranges to \[2l + 1\] . And m ranges from –l to l in continuous integer format. By this we will get the correct set of answers for the following

Complete step by step answer:
Now we have to implement the formulas and the ideas regarding the quantum numbers we possess to enlist the right set of values. We will deal with it step by step to ensure correctness and will take every quantum number one by one.
Now let's take the step by step analysis of this:
Step 1: firstly we have to take care of the values we have. Here we have the value of \[l{\text{ }} = {\text{ }}2\]
And we know that, \[m{\text{ }} = {\text{ }} - l, \ldots ,0,..,l\]
Step 2: Therefore, this will give us the final and required value of \[m{\text{ }} = {\text{ }} - 2, - 1,0,1,2\] , by the principle used for the finding.
Hence the correct answer would be option A, \[\; - 2, - 1,0,1,2\] .

Note:
Magnetic Quantum Number is the one that specifies the orientation in space of an orbital of a given energy (n) and shape (l). This number also divides the subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell. Thus we can say that the s subshell has only one orbital, the p subshell has three orbitals, and so on.