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  • A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ. An alpha particle having certain kinetic energy has the same de-Brogle wavelength &lambda

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ. An alpha
particle having certain kinetic energy has the same de-Brogle wavelength λ. The ratio of kinetic energy
of proton and that of alpha particle is:

Option: 1

2: 1


Option: 2

 1: 2 


Option: 3

 1: 4


Option: 4

 4: 1


Answers (1)

best_answer

The wavelength of matter is given by

\begin{aligned} & \lambda=\frac{\mathrm{h}}{\mathrm{p}} \\ & \frac{\lambda_{\mathrm{p}}}{\lambda_\alpha}=\frac{\mathrm{p}_\alpha}{\mathrm{p}_{\mathrm{p}}}=\frac{\sqrt{2 \mathrm{k}_{\mathrm{a}} \mathrm{m}_\alpha}}{\sqrt{2 \mathrm{k}_{\mathrm{p}} \mathrm{m}_{\mathrm{p}}}}=1 \\ & \therefore \frac{\mathrm{k}_\alpha}{\mathrm{k}_{\mathrm{p}}} \times \frac{\mathrm{m}_\alpha}{\mathrm{m}_{\mathrm{p}}}=1 \Rightarrow \frac{\mathrm{k}_\alpha}{\mathrm{k}_{\mathrm{p}}}=\frac{\mathrm{m}_{\mathrm{p}}}{\mathrm{m}_\alpha} \\ & \frac{\mathrm{k}_\alpha}{\mathrm{k}_{\mathrm{p}}}=\frac{1}{4} \end{aligned}

Posted by

Shailly goel

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