Question

What set of quantum numbers is not possible? $n,l,{m_l},{m_s}$
A) $2,{\text{ }}1,{\text{ }}1,{\text{ }}1/2$
B) $2,{\text{ }}1,{\text{ - }}1,{\text{ }}1/2$
C) $3,{\text{ 2}},{\text{ 2}},{\text{ }}1/2$
D) $3,{\text{ 3}},{\text{ - 3}},{\text{ }}1/2$

Answer 1

Hint: Quantum number is defined as the set of numbers that describes the probable location of the electron in an atom. There are four main quantum numbers. Each quantum number signifies a specific feature of the atom. Principle quantum number is for the shell, angular momentum quantum number is for the subshell, magnetic quantum number is for the orbital and spin quantum number is for the spin of the electron.

Complete answer:
Each electron in atom is described by a set of four numbers
1) Principal quantum number (n)
2) Angular momentum quantum number (l)
3) Magnetic quantum number $({m_l})$
4) Spin quantum number $({m_s})$
As the value of the angular momentum quantum number is equal $l = n - 1$, so the possible values for angular momentum quantum number are –
$\eqalign{ & n = 1,l = 0 \cr & n = 2,l = 0,1 \cr & n = 3,l = 0,1,2 \cr & n = 4,l = 0,1,2,3 \cr} $
So, the given values of angular momentum quantum number with respect to principal quantum number are correct only for option A, B and C.
In option D, the given value of angular momentum quantum number is not valid for the $n = 3$.

Hence, the set of quantum numbers is not possible is D) $3,{\text{ 3}},{\text{ - 3}},{\text{ }}1/2$

Note:
The most well-known system of nomenclature arose from Friedrich Hund and Robert S. Mulliken's molecular orbital theory, which combines Bohr energy levels as well as electron spin data. This model uses four quantum numbers to characterise electrons: energy (n), angular momentum (l), magnetic moment (ml), and spin (ms). In the classical description of nuclear particle states, it is also the standard terminology of protons and neutrons.