Q144 / 150 · MHT CET 2024 (10 May Shift 1) · Physics
If the potential difference used to accelerate electrons is increased four times, by what factor does the de-Broglie wavelength associated with the electrons change?
- AWavelength increased two times
- Correct answerBWavelength decreased to half
- CWavelength increased four times
- DWavelength remains the same
Solution
$\begin{array}{ll}
& \lambda \propto \frac{1}{\sqrt{\mathrm{~V}}} \\
\therefore & \frac{\lambda_2}{\lambda_1}=\sqrt{\frac{\mathrm{V}_1}{\mathrm{~V}_2}}
\end{array}$
Given that, $\mathrm{V}_2=4 \mathrm{~V}_1$ $\therefore \quad \lambda_2=\lambda_1 \times \sqrt{\frac{\mathrm{V}_1}{4 \mathrm{~V}_1}}=\frac{\lambda_1}{2}$
Given that, $\mathrm{V}_2=4 \mathrm{~V}_1$ $\therefore \quad \lambda_2=\lambda_1 \times \sqrt{\frac{\mathrm{V}_1}{4 \mathrm{~V}_1}}=\frac{\lambda_1}{2}$
Hence, the correct answer is option: 'B'.