Question

Which set of quantum numbers are consistent with the theory?
A.n = 2, l = 1, m = 0, s = -1/2
B.n = 4, l = 3, m = -2, s = -1/2
C.n = 3, l = 2, m = -3, s = +1/2
D.n = 4, l = 3, m = -3, s = +1/2

Answer 1

Hint:There are four different types of quantum numbers. The values of the different quantum numbers lie in various ranges. We will check this range or the permissible values of the quantum numbers and will answer the question.

Complete answer:
n denotes principal quantum number. Principle quantum number denotes the state of the electron. It can have any whole number as its values.
l denotes azimuthal quantum number. The azimuthal quantum number is a quantum number for an atomic orbital that determines its orbital angular momentum and describes the shape of the orbital. It has values from 0 to (n-1).
m denotes magnetic spin quantum number. Specifies the orientation in space of an orbital of a given energy (n) and shape (l). This number divides the subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell. It has values from –l to +l.
s denotes spin quantum number. The spin quantum number is a quantum number that parametrizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle. It can have value either +1/2 or 1/2.
Now we will check the options.
The first option follows all the criteria. So it is correct.
The second option follows all the criteria. So it is correct.
The third option does not follow all the criteria as m does not lie between –l to +l. So it is incorrect.
The fourth option follows all the criteria. So it is correct.

Hence option A, B and D are correct.

Note:
The range of values or the permissible values for all the quantum numbers should be known. With this information this kind of question can easily be solved. No two electrons can have all the four same quantum numbers. This is Pauli's Exclusion Principle.