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An electron is continuously accelerated in a vacuum tube by the application of a potential differencAtomic Structure Chemistry Question

Question

An electron is continuously accelerated in a vacuum tube by the application of a potential difference. If its de-Broglie wavelength decreases by 1% over a path length of $l$ cm, its kinetic energy

Answer: B

💡 Solution & Explanation

Wavelength $\lambda = \frac{h}{\sqrt{2mK}} \implies K \propto \frac{1}{\lambda^2}$. If $\lambda$ decreases by 1%, the new wavelength is $0.99\lambda$. New kinetic energy $K' = \frac{K}{0.99^2} \approx \frac{K}{0.9801} \approx 1.02 K$. This corresponds to an increase of roughly 2%. Therefore, correct answer is B.

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