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(C) The de Broglie wavelength $(\lambda)$ of an electron accelerated through a potential difference $V$ is given by the formula: $\lambda = \frac{h}{\

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$\lambda$ is decreased by $\frac{1}{\sqrt{2}}$ times.

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(C) The de Broglie wavelength $(\lambda)$ of an electron accelerated through a potential difference $V$ is given by the formula: $\lambda = \frac{h}{\sqrt{2mqV}}$.From this relation,we can see that $\lambda \propto \frac{1}{\sqrt{V}}$.Let the initial potential be $V_1 = V$ and the final potential be $V_2 = 2V$.The ratio of the wavelengths is $\frac{\lambda_2}{\lambda_1} = \sqrt{\frac{V_1}{V_2}} = \sqrt{\frac{V}{2V}} = \frac{1}{\sqrt{2}}$.Therefore,the new wavelength $\lambda_2 = \frac{1}{\sqrt{2}} \lambda_1$.Thus,the de Broglie wavelength is decreased by a factor of $\frac{1}{\sqrt{2}}$.

If the potential difference used to accelerate electrons is doubled,by what factor does the de Broglie wavelength $(\lambda)$ associated with the electrons change?

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