# Q12  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        $1.67 \times 10 ^{-27} Kg , 1 e V = 1.60 \times 10 ^{-19} J$)

D Devendra Khairwa

The kinetic energy of the electron is given by :

$K_e\ =\ \frac{1}{2}mv_e^2$

or                                             $1.6\times 10^{-15}\ J\ =\ \frac{1}{2}\times 9.11\times 10^{-31}\times v_e^2$

Thus velocity is obtained as :

$v_e\ =\ \sqrt{\frac{2\times 1.6\times 10^{-15}}{9.11\times 10^{-31}}}$

or                                                               $=\ 5.93\times 10^7\ m/s$

Similarly, we can find the velocity of the proton :

$K_p\ =\ \frac{1}{2}mv_p^2$

$1.6\times 10^{-14}\ J\ =\ \frac{1}{2}\times 1.67\times 10^{-27}\times v_p^2$

Thus velocity is obtained as :

$v_p\ =\ \sqrt{\frac{2\times 1.6\times 10^{-14}}{1.67\times 10^{-27}}}$

or                                                               $=\ 4.38\times 10^6\ m/s$

Thus the ratio of their velocities is :

$\frac{v_e}{v_p}\ =\ \frac{5.93\times 10^{7}}{4.38\times 10^6}\ =\ 13.54$

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