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  • An  and proton have the same kinetic energy, the ratio of de Brogli

An \alpha-\mathrm{particle} and proton have the same kinetic energy, the ratio of de Broglie wavelength of  \alpha-\mathrm{particle} and proton is:

 

Option: 1

2


Option: 2

1


Option: 3

1/2


Option: 4

1/4


Answers (1)

best_answer


Kinetic energy K is related with momentum (p) of the particle by the relation, K=\frac{\mathrm{p}^2}{2 \mathrm{~m}}

or \mathrm{p}=\sqrt{2 \mathrm{mK}}

\therefore \quad de Broglie wavelength 

\begin{aligned} &\lambda=\frac{\mathrm{h}}{\mathrm{p}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{mK}}};\\ &\text{ So } \lambda \propto \frac{1}{\sqrt{\mathrm{m}}}\\ &\therefore \frac{\lambda_\alpha}{\lambda_{\mathrm{p}}}=\sqrt{\frac{\mathrm{m}_{\mathrm{p}}}{\mathrm{m}_\alpha}}=\sqrt{\frac{1}{4}}=\frac{1}{2} \end{aligned}

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Rishi

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