If the potential difference used to accelerate electrons is doubled. By what factor does the deBroglie…
If the potential difference used to accelerate electrons is doubled. By what factor does the deBroglie wavelength $(\lambda)$ associated with the electrons change?
$\lambda$ is increased to $\sqrt{2}$ times.
$\lambda$ is increased to $\frac{1}{\sqrt{2}}$ times.
$\lambda$ is decreased by $\frac{1}{\sqrt{2}}$ times.
$\lambda$ is decreased by $\sqrt{2}$ 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.