Question

If ${{m}_{l}}$= magnetic quantum number and l = Azimuthal quantum number then:
[A] ${{m}_{l}}=l+2$
[B] ${{m}_{l}}=2{{l}^{2}}+1$
[C] $l=\dfrac{{{m}_{l}}-1}{2}$
[D] $l=2{{m}_{l}}+1$

Answer 1

Hint: To answer this you must know that Azimuthal quantum number describes the subshell and it is related to magnetic quantum number. The magnetic quantum number varies from -l to +l. You can use this to answer the given question.

complete step by step answer:
We know that to completely describe an atom, four quantum numbers are introduced. Two among these 4 are azimuthal quantum number and magnetic quantum number. Let us discuss about them briefly and then try to find out the relation between them
Azimuthal quantum number is denoted as ‘l’ and it is also known as angular or orbital quantum number. It describes the subshell and gives us the magnitude of orbital angular momentum. For s, p, d and f orbital, the value of l is 0, 1, 2 and 3 respectively.
Magnetic quantum number is denoted by ${{m}_{l}}$ and it describes the energy levels available within a subshell and it also yields the projection along a specified axis of the orbital angular momentum. It is associated with the orientation of the orbitals.
Now, let us see the relation between the two.
Magnetic and Azimuthal quantum numbers are related to each other. If l = 2 then ${{m}_{l}}$ can get any value from -2 to +2 i.e. -2, -1, 0, +1 and +2. We can say that the value of ${{m}_{l}}$ ranges from -l to +l. So, we can also write that for l = 2, m = 5 or we can also write it as (2l + 1).
So, the relation is: m = 2l + 1
Or, m – 1 = 2l
Or, $\dfrac{m-1}{2}=l$
The above relation is valid for any value of l.
Therefore, the correct answer is option [C] $l=\dfrac{{{m}_{l}}-1}{2}$.


Note: Besides azimuthal quantum number and magnetic quantum number, there are two more quantum numbers namely principle quantum number and spin quantum number. The principal quantum number is denoted as ‘n’ and it describes the electron shell or energy level of an atom. Its value ranges from 1 to the shell containing the outermost electron. Spin quantum number is denoted as ${{m}_{s}}$ and it describes the spin of the electron within the orbital. It’s value for an electron is $\pm \dfrac{1}{2}$.