A proton and an electron have the same de Broglie wavelength. If \(K_p\) and \(K_e\) be the kinetic energies of proton and electron respectively. Then choose the correct relation :

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Answer & Solution

Correct Answer

(D) \(\mathrm{K}_{\mathrm{p}}<\mathrm{K}_{\mathrm{e}}\)

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Detailed explanation

De Broglie wavelength of proton & electron \(=\lambda\)

\(\because \lambda=\frac{\mathrm{h}}{\mathrm{p}}\)

\(\therefore \mathrm{p}_{\text {proton }}=\mathrm{p}_{\text {electron }}\)

\(\because \mathrm{KE}=\frac{\mathrm{p}^2}{2 \mathrm{~m}}\)

\(\therefore \mathrm{KE}_{\text {proton }}<\mathrm{KE}_{\text {electron }}\)

\({\left[\mathrm{K}_{\mathrm{p}}<\mathrm{K}_{\mathrm{e}}\right]}\)

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