Question

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy $10 \,keV$, and the second with $100 \,keV$. The ratio of their speeds is (where $m_e$ and $m_p$ are masses of electron and proton respectively)

• A. $\sqrt{\frac{1}{10} \frac{m_{e}}{m_{p}}}$
• B. $\sqrt{\frac{1}{10} \frac{m_{p}}{m_{e}}}$
• C. $\\\frac{1}{10} \frac{m_{e}}{m_{p}}$
• D. $\frac{1}{10} \frac{m_{e}}{m_{p}}$

Answer 1

Answer: (B)

$\sqrt{\frac{1}{10} \frac{m_{p}}{m_{e}}}$

Answer 2

Kinetic energy of the electron, $K_{e} = \frac{1}{2}m_{e}v^{2}_{e} = 10\,eV\quad\cdots\left(i\right)$ Kinetic energy of the proton, $K_{p} = \frac{1}{2}m_{p}v^{2}_{p} = 100eV\quad\cdots\left(ii\right)$ Divide $\left(i\right)$ by $\left(ii\right)$, we get $\frac{m_{e}v^{2}_{e}}{m_{p}v^{2}_{p}} = \frac{1}{10}$ or $\frac{v^{2}_{e}}{v^{2}_{p}} = \frac{1}{10} \frac{m_{p}}{m_{e}}$ or $\frac{v_{e}}{v_{p}} = \sqrt{\frac{1}{10} \frac{m_{p}}{m_{e}}}$