Question

An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy $10keV$, and the second with $100keV$. 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. $frac110\frac{m_e}{m_p}$
• D. $\frac{1}{10}\frac{m_e}{m_p}$

Answer 1

Answer: (B)

Kinetic energy of the electron,
$K_e=\frac{1}{2}{m}_e{v}_e^2=10eV\cdots \left(i\right)$
Kinetic energy of the proton,
$K_p=\frac{1}{2}{m}_p{v}_p^2=100eV\cdots \left(ii\right)$
Divide $\left(i\right)$ by $\left(ii\right)$, we get
$\frac{m_e{v}_e^2}{m_p{v}_p^2}=\frac{1}{10}$
or $\frac{v_e^2}{v_p^2}=\frac{1}{10}\frac{m_p}{m_e}$
or $\frac{v_e}{v_p}=\sqrt{\frac{1}{10}\frac{m_p}{m_e}}$