Question

Assertion :If the potential difference applied to an electron is made $4$ times, the de Broglie wavelength associated is halved. Reason: On making potential difference $4$ times, velocity is doubled and hence $d$ is halved.

• 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

$\lambda =\frac{h}{\sqrt{2mqV}}$ Thus $\lambda \propto \frac{1}{\sqrt{V}}\therefore$ on making potential difference $4$ times, $\lambda$ is halved, also $V=\sqrt{\frac{2qV}{m}}$ thus on making V $4$ times V is doubled and $\lambda =\frac{h}{mv}\Rightarrow \lambda \propto \frac{1}{V}$.

Hence $\lambda$ is halved. Thus correct option is A.