Question

Each question contains statement 1 and statement 2. Choose the correct answer (only one option is correct) from the following options.

Statement-1 : The de-Broglie wavelength of a molecule (in a sample of ideal gas) varies inversely as the square root of absolute temperature.
Statement-2 : The rms velocity of a molecule (in a sample of ideal gas) depends on temperature.

• A. Statement-1 is false, Statement -2 is true
• B. Statement -1 is true, Statement-2 is true; Statement -2 is a correct explanation for statement-1
• C. Statement-1 is true, Statement -2 is false
• D. Statement -1 is true, Statement-2 is true; Statement -2 is not correct explanation for statement-1

Answer 1

Answer: (B)

$v_{rms}=\sqrt{\frac{3RT}{M}}$

$v_{rms}\propto \sqrt{T}$

De broglie wavelength
$\lambda =\frac{h}{mv}$
$\lambda \propto \frac{1}{v_{rms}}$
$\lambda \propto \frac{1}{\sqrt{T}}$