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  • A proton and an α-particle are accelerated, using the same potential difference. How are the de Broglie wavelengths λp and λa related to each other?

A proton and an \alpha-particle are accelerated, using the same potential difference. How are the de Broglie wavelengths \lambda_{p} and \lambda_{a} related to each other?

Answers (1)

It is given that the proton and \alpha-particle are accelerated at the

 same potential difference so their kinetic energies will be equal.  

K_{1}=K_{2}=K=qV\\ \lambda=\frac{h}{\sqrt{2mK}}=\frac{h}{\sqrt{2mqV}}\\ \frac{\lambda_{p}}{\lambda_{a}}=\sqrt{\frac{m_{a}q_{a}V_{a}}{m_{p}q_{p}V_{p}}}\\ m_{a}=4m_{p};q_{a}=2e;q_{p}=e;V_{p}=V_{a}=V\\ \frac{\lambda_{p}}{\lambda_{a}}=\sqrt{\frac{4m_{p}2eV}{m_{p}eV}}=\sqrt{8}\\ \lambda_{p}=\sqrt{8}\lambda_{\alpha }

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