If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie…
If the potential difference used to accelerate electrons is doubled, by what factor does the de-Broglie wavelength associated with electrons change?
Wavelength in increased to $\frac{1}{\sqrt{2}}$ times.
Wavelength in increased to $\frac{1}{2}$ times.
Wavelength in decreased to $\frac{1}{\sqrt{2}}$ times.
Wavelength in decreased to $\frac{1}{2}$ times.
Solution
From $\lambda=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mqV}}}$,
$\lambda \propto \frac{1}{\sqrt{V}}$
If potential difference is doubled, $\lambda \propto \frac{1}{\sqrt{2 \mathrm{~V}}}$
$\therefore \quad \lambda$ is decreased by $\frac{1}{\sqrt{2}}$ times.