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 `=9.11xx10^(-31) kg`, proton mass `=1.67xx10^(-27) kg, 1 eV=1.60xx10^(-19) J)`.

Explanation

Here, `K_(e)= 10keV` and `K_(p)` = 100 keV
`m_(e)= 9.11 xx 10^(-31)` kg and `m_(p) = 1.67 xx 10^(-27)` kg
As `K=1/2mv^(2)` or `v=sqrt((2K)/m)`,
Hence, `v_(e)/v_(p) = sqrt(K_(e)/K_(p) xx m_(p)/m_(e)) = sqrt((10keV)/(100 keV) xx (1.67 xx 10^(-27)kg)/(9.11 xx 10^(-31))kg)`
=13.54
`rArr v_(e) = 13.54 v_(p)`.
Thus, electron is travelling faster.