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Magnetic Properties of Matter question

2019 · 12 Jan · Shift 2 · Q56
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Magnetic Properties of Matter question

2019 · 12 Jan · Shift 2 · Q56

JEE MainPhysicsMagnetic Properties of MatterMCQ+4 / −1
A paramagnetic material has 1028 atoms/m3. Its magnetic susceptibility at temperature 350 K is 2.8 ×\times× 10–4. Its susceptibility at 300 K is :
  1. A
    3.726 ×\times× 10–4
  2. B
    2.672 ×\times× 10–4
  3. C
    3.672 ×\times× 10–4
  4. D
    3.267 ×\times× 10 −-− 4
View written solutionFree

Correct answer: D

  1. Use Curie’s law for a paramagnetic material

For a paramagnetic substance,

χ∝1T\chi \propto \frac{1}{T}χ∝T1​

So,

χT=constant\chi T = \text{constant}χT=constant

Hence,

χ1T1=χ2T2\chi_1 T_1 = \chi_2 T_2χ1​T1​=χ2​T2​
  1. Given data

At temperature T1=350 KT_1 = 350\,\text{K}T1​=350K,

χ1=2.8×10−4\chi_1 = 2.8 \times 10^{-4}χ1​=2.8×10−4

We need susceptibility at

T2=300 KT_2 = 300\,\text{K}T2​=300K
  1. Apply Curie’s law
χ2=χ1T1T2\chi_2 = \chi_1 \frac{T_1}{T_2}χ2​=χ1​T2​T1​​

Substitute values:

χ2=2.8×10−4×350300\chi_2 = 2.8 \times 10^{-4} \times \frac{350}{300}χ2​=2.8×10−4×300350​ χ2=2.8×10−4×76\chi_2 = 2.8 \times 10^{-4} \times \frac{7}{6}χ2​=2.8×10−4×67​ χ2=3.2666…×10−4\chi_2 = 3.2666\ldots \times 10^{-4}χ2​=3.2666…×10−4

So,

χ2≈3.267×10−4\chi_2 \approx 3.267 \times 10^{-4}χ2​≈3.267×10−4
  1. Match with options

The correct option is:

D: 3.267×10−4\boxed{\text{D: } 3.267 \times 10^{-4}}D: 3.267×10−4​
  1. Comparison with stored answer

Stored correct answer: D

This matches our derived answer.

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