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?

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Aicharya · Accepted Answer

$\begin{array}{ll} & \lambda \propto \frac{1}{\sqrt{\mathrm{~V}}} \\ \therefore & \frac{\lambda_2}{\lambda_1}=\sqrt{\frac{\mathrm{V}_1}{\mathrm{~V}_2}} \end{array}$
Given that, $\mathrm{V}_2=4 \mathrm{~V}_1$ $\therefore \quad \lambda_2=\lambda_1 \times \sqrt{\frac{\mathrm{V}_1}{4 \mathrm{~V}_1}}=\frac{\lambda_1}{2}$

If the potential difference used to accelerate electrons is increased four times, by what factor does the…

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