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

Kinetic energy of electron ` = 1/2 m_(e)v_(e)^(2)`
` 10 xx 10^(3) xx1.60 xx10^(-19)J = 1/2 xx 9.11 xx10^(-31)v_(e)^(2) " " …(i)`
Kinetic energy of proton ` = 1/2 m_(p)v_(p)^(2)`
` 100 xx 10^(3) xx1.60 xx10^(-19) J = 1/2 xx1.67 xx10^(-27)v_(p)^(2)" " ...(ii)`
Dividing (i) by (ii) , we get
` (10 xx 10^(3) xx1.60 xx10^(-19))/(100 xx 10^(3)xx1.60 xx10^(-19)) = (1/2 xx9.11xx10^(-31)v_(e)^(2))/(1/2 xx1.67 xx10^(-27)v_(p)^(2))`
`(v_(e)^(2))/(v_(p)^(2)) = (1670)/(9.11)`
`(v_(e))/(v_(p)) = sqrt((1670)/(9.11)) = 13.53 `
Thus , the electron moves faster than proton .