Question

Based on the above assumption, magnetic moment of the element with atomic number 18 is:
(A) $\sqrt {24} {\text{BM}}$
(B) $\sqrt 8 {\text{BM}}$
(C) ${\text{Zero BM}}$
(D) $\sqrt {15} {\text{BM}}$

Answer 1

To answer this question, you must recall the formula for calculating the magnetic moment of an element. To find the magnetic moment it is important to write the electronic configuration of the element.
Formula used: $\mu = \sqrt {n\left( {n + 2} \right)}$
Where, $\mu$ represents the magnetic moment of the element
And $n$ represents the number of unpaired electrons in its valence shell.

Complete step by step solution
First we must write the electronic configuration of the given element. The electronic configuration of an element depends on three rules namely, the Hund’s rule, Pauli’s exclusion principle and Auf- bau principle.
The Hund’s rule of maximum multiplicity: It states that all orbitals in a sub- shell are first singly- filled before pairing of electrons starts.
The Pauli’s exclusion principle: It states that each electron has a different set of quantum numbers associated to it.
The Auf- bau principle: It states that atomic orbitals in an atom are filled in the increasing order of the energy level of the orbitals.
Using the above mentioned rules, the electronic configuration for the element with atomic number 18 can be written as
$\left( {Z = 18} \right)1{s^2}2{s^2}2{p^6}3{s^2}3{p^6}$
From the electronic configuration, we can see that all the electrons are paired. So $n = 0$
Thus, the magnetic moment of the element is given by $\mu = 0$
Thus, the correct answer is C.

Note
The unit of magnetic moment is Bohr Magneton or BM. It represents the moment of the electron. There is another quantity known as neutron magneton which represents the moment of the nuclei, protons and neutrons. The magnetic moment for electrons can also be calculated using the spin quantum number of the electrons. Its formula is given as $\mu = \sqrt {4s\left( {s + 1} \right)} {\text{BM}}$