Question

What are the possible values of $ n $ and $ ml $ for an electron in a $ 5d $ orbital ?
(A) $ n=5 $ and $ ml=-2,-1,0,+1or+2 $
(B) $ n=1,2,3,4or5 $ and $ ml=2 $
(C) $ n=5 $ and $ ml=2 $
(D) $ n=1,2,3,4\,or\,5 $ and $ ml=-2,-1,0,+1\,or\,+2$

Answer 1

Hint: To solve the given question, the concepts to be cleared are about Quantum number, shells, sub-shells, orbitals.
Quantum number is basically the address of an electron in an atom.Shells are the permitted orbits where an electron revolves with fixed angular momentum. Subshell is a division under a shell which contains orbital or orbitals.

Complete step by step solution:
Step-1 :
Here, the peripheral quantum number, $ n $ denotes the number of shells. It is the number written with the orbital. It gives the distance of the electron cloud from the nucleus i.e. the size of the orbital. Here, the number of orbitals allowed is equal to $ n^2 $ .
Step-2 :
$ ml $ is the magnetic quantum number whose value ranges from $ -l $ to $ +l $ . If $ l=2; m=-1,0,+1 $ and the number of orbitals equal to $ 3 $.
Step-3 :
$ l $ is the Azimuthal quantum number, whose value is from $ 0 $ to $ n-1 $ .
Considering all the steps, we can say that $ 5d $ has $ n=5,l=2 $ so $ m=-2,-1,0,+1\,or\,+2 $ .
Hence, option (A) is correct.

Additional Information:
The four quantum numbers are Principal Quantum Number which denotes the shell, Azimuthal Quantum Number denoting sub-shell, Magnetic Quantum Number and Spin Magnetic Number.
The sub-shells are s,p,d,f, . . . . . . and so on. They are filled on the basis of energy with the $ n+l $ rule.

Note:
The magnetic quantum number basically determines the spatial orientation of the orbital along the axis. The number of allowed orbitals is $ 2l+1 $ and orbital angular momentum is $ \sqrt{l+(l+1)} \dfrac { h }{ 2\pi }. $