Question

Spin multiplicity of nitrogen in ground state will be ……………
A. $4$
B. $3$
C. $5$
D. $0$

Answer 1

Hint: Hund’s Rule is also known as Hund’s rule of maximum spin multiplicity. According to this rule the pairing of electrons only takes place once the electrons are completely half filled in the orbital.


Complete step by step solution:
According to Hund’s rule the different electrons are filled in different orbitals of a sub – shell in such a way to give a maximum number of unpaired electrons with parallel spin.
This rule can also be written as,
The electrons are filled in different orbitals of a sub – shell so that the value of spin multiplicity is maximum.
Once all the orbitals sub – shell are singly occupied with parallel spin then pairing of electrons occurs.
Spin multiplicity is based on the number of unpaired electrons and each unpaired electron has $ \pm 1/2$value.
If no unpaired electron will become singlet$\left( 1 \right)$.
Formula used:
Spin multiplicity $\left( {{S_m}} \right) = 2 \times \left| {{S_T}} \right| + 1$
Where, ${S_T}\xrightarrow{{}}Total{\text{ spin}}$
Nitrogen has atomic number$7$. It means the number of protons and number of electrons both are equal to$7$.
$_7N:$ Atomic number $ = 7$
Number of proton $ = 7$
Number of electron $ = 7$
Electronic configuration of nitrogen in ground state –
$7N:{\text{ 1}}{{\text{S}}^2}{\text{ 2}}{{\text{s}}^2}{\text{ }}\mathop {{\text{2}}{{\text{p}}^3}}\limits_{\boxed \uparrow \boxed \uparrow \boxed \uparrow } $
Nitrogen has $3$ unpaired electrons in its outermost shell.
So, total spin.
$
  {S_T} = \left| { + \dfrac{1}{2} + \dfrac{1}{2} + \dfrac{1}{2}} \right| \\
  {S_T} = \left| { + \dfrac{3}{2}} \right| \\
 $
Put the value of ${S_T}$
Spin multiplicity $\left( {{S_m}} \right) = 2 \times \left| {{S_T}} \right| + 1$
$
   = 2 \times \dfrac{3}{2} + 1 \\
   = 3 + 1 \\
  {S_m} = 4 \\
 $
Hence, the correct option is (A).


Note: We use Hund’s rule for this question Hund’s rule based on spin multiplicity and it depends on the number of unpaired electrons. Each unpaired electron has $ + \dfrac{1}{2}$ spin value. Spin multiplicity value of any atom or compound reflects its magnetic nature as well. The atoms with unpaired electrons are called as paramagnetic. Here, nitrogen has three unpaired electrons so it is a paramagnetic compound.