What should be the increase in kinetic energy, of electron in order to decrease its de-Broglie wavel — Atomic Structure Chemistry Question

💡 Solution & Explanation

Wavelength decreases by a factor of 2, so kinetic energy must increase by a factor of $2^2 = 4$. Increase is $\Delta K = 4K - K = 3K$. Initial $K = \frac{hc^2}{2mc^2 \lambda^2} = \frac{(1240 \text{ eV}\cdot\text{nm})^2}{2 \times 0.511 \times 10^6 \text{ eV} \times (100 \text{ nm})^2} \approx 1.5 \times 10^{-4}$ eV. $\Delta K = 3 \times 1.5 \times 10^{-4} = 4.5 \times 10^{-4}$ eV. Therefore, correct answer is B.