Question

Given below are two statements:
Assertion (A): The Einstein specific heat \((C_V)\), at low temperature is, \[ C_V=3NK\left(\frac{h\nu}{KT}\right)^3\exp\left(-\frac{h\nu}{KT}\right) \]
Reason (R): The Einstein specific heat, at high temperature, is \(C_V=3NK\).

• A. Both A and R are correct and R is the correct explanation of A
• B. Both A and R are correct but R is not the correct explanation of A
• C. A is correct but R is not correct
• D. A is not correct but R is correct

Hint:

At high temperature, Einstein specific heat approaches \(3NK\), which agrees with Dulong-Petit law.

Answer 1

The Correct Option is D

Concept:
Einstein theory of specific heat explains the variation of specific heat of solids with temperature.

Step 1: Check Assertion.
At low temperature, Einstein specific heat decreases exponentially. The standard low temperature dependence contains an exponential term and a power factor, but the expression given in Assertion is not the correct standard expression. \[ A \text{ is not correct} \]

Step 2: Check Reason.
At high temperature, Einstein's specific heat approaches the classical Dulong-Petit value: \[ C_V=3NK \] So, \[ R \text{ is correct} \]

Step 3: Final conclusion.
Assertion is incorrect but Reason is correct. \[ \therefore \text{Correct Answer is (D)} \]