An electron and a proton are detected in a cosmic ray experiment,the first with kinetic energy $10 \; keV$,and the second with $100 \; keV$. Which is faster,the electron or the proton? Obtain the ratio of their speeds. (Electron mass $= 9.11 \times 10^{-31} \; kg$,proton mass $= 1.67 \times 10^{-27} \; kg$,$1 \; eV = 1.60 \times 10^{-19} \; J$)

(N/A) The electron is faster. The ratio of their speeds is $13.54:1$.
Given:
Mass of the electron,$m_e = 9.11 \times 10^{-31} \; kg$
Mass of the proton,$m_p = 1.67 \times 10^{-27} \; kg$
Kinetic energy of the electron,$E_{Ke} = 10 \; keV = 10^4 \; eV = 1.60 \times 10^{-15} \; J$
Kinetic energy of the proton,$E_{Kp} = 100 \; keV = 10^5 \; eV = 1.60 \times 10^{-14} \; J$
Using the formula for kinetic energy $E_K = \frac{1}{2}mv^2$,the velocity is $v = \sqrt{\frac{2E_K}{m}}$.
For the electron:
$v_e = \sqrt{\frac{2 \times 1.60 \times 10^{-15}}{9.11 \times 10^{-31}}} \approx 5.93 \times 10^7 \; m/s$
For the proton:
$v_p = \sqrt{\frac{2 \times 1.60 \times 10^{-14}}{1.67 \times 10^{-27}}} \approx 4.38 \times 10^6 \; m/s$
Comparing the velocities,$v_e > v_p$,so the electron is faster.
The ratio of their speeds is $\frac{v_e}{v_p} = \frac{5.93 \times 10^7}{4.38 \times 10^6} \approx 13.54$.