Answer –

We are given the number of diatomic dipoles =  2.0 × 10²⁴

Dipole moment of each dipole is given by M’= 1.5 × 10^–23 J T^–1

Magnetic field strength is given by B₁= 0.64 T

Cooled to a temperature which is given by T₁= 4.2 K

Total dipole moment of the sample can be found out by using the following relation

n x M’ = 2.0 × 10²⁴  x1.5 × 10^–23 

n x M’  = 30

Degree of magnetic saturation, given = 15 %

Therefore,

M₁ = (15/100) x 30 = 4.5 J/T

Magnetic field strength is given by  B₂ = 0.98 T

Temperature, T₂ = 2.8 K

The ratio of magnetic dipole from Curie temperature can be written as –

\[\frac{{{M}_{2}}}{{{M}_{1}}}=\frac{{{B}_{2}}}{{{B}_{1}}}\times \frac{{{T}_{1}}}{{{T}_{2}}}\]

\[{{M}_{2}}={{M}_{1}}\frac{{{B}_{2}}}{{{B}_{1}}}\times \frac{{{T}_{1}}}{{{T}_{2}}}\]

\[{{M}_{2}}=4.5\times \frac{0.98}{0.64}\times \frac{4.2}{2.8}\]

\[{{M}_{2}}=10.34J{{T}^{-1}}\]