The ratio of the de Broglie wavelengths of two identical electrons accelerated from rest through pot — Atomic Structure Chemistry Question

💡 Solution & Explanation

The de Broglie wavelength of an electron accelerated by potential $V$ is inversely proportional to $\sqrt{V}$, i.e., $\lambda \propto \frac{1}{\sqrt{V}}$. Therefore, $\frac{\lambda_1}{\lambda_2} = \sqrt{\frac{V_2}{V_1}} = \sqrt{\frac{50}{200}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$. Given that the ratio is $\frac{x}{2}$, it follows that $x = 1$.