Question

Assertion :The de Broglie wavelength of a molecule varies inversely as the square root of temperature. Reason: The root mean square velocity of the molecule depends on the temperature.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

Root mean square speed

$v_{rms}=\sqrt{\frac{3kT}{m}}$

Most probable speed

$v_{mp}=\sqrt{\frac{2kT}{m}}$

Average speed

$v_{av}=\sqrt{\frac{8kT}{\pi m}}$

So, $v_{rms}$ of gas molecule $\propto \sqrt{T}$

The de-broglie equation is

$\lambda =\frac{h}{mv}=\frac{h}{m\times K\sqrt{T}}$ [$K$ is a constant]

So, $\lambda \propto \frac{1}{\sqrt{T}}$

So both reason and assertion is true.