Question

The magnetic susceptibility of a paramagnetic material at –73 °C is 0.0075 . What will be the magnetic susceptibility at –173 °C?
1. 0.005
2. 0.015
3. 0.025
4. 0.055

Answer 1

Correct Answer - Option 2 : 0.015

The correct answer is option 2) i.e. 0.015

CONCEPT:

• Magnetic susceptibility: Magnetic susceptibility (χ) is a measure of the degree of magnetization of a material under an external magnetic field.
  • ​It is related to the magnetization (M) and magnetizing field (H) as follows

​\(χ = \frac{M}{H}\)

• Paramagnetic substances: Paramagnetic substances are those substances that get weakly magnetized with the influence of an external magnetic field.
  • ​A paramagnetic atom has spin and orbital magnetic moments aligned in such a way that they have a permanent magnetic dipole moment.
  • However, due to the thermal vibrations of the atoms, these magnetic moments get aligned in random directions such that the net magnetic moment is zero.
  • Under the influence of an external magnetic field, they tend to get slowly aligned along the direction of the field.
  • The magnetic susceptibility of a paramagnet is inversely proportional to the value of the absolute temperature on the Kelvin scale. 

​
CALCULATION:

Given that:

Magnetic susceptibility, χ₁= 0.0075

Temperature, T₁ = –73 °C = 200 K

Temperature, T2 = –173 °C = 100 K

Magnetic susceptibility of a paramagnet is inversely proportional to the value of the absolute temperature \(⇒χ = \frac{1}{T}\)

⇒ χT = constant

χ₁T₁ = χ₂T₂

⇒ (0.0075 × 200) = (χ2 × 100)

⇒  χ2 = 0.015