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

Explanation

`(K_(e))/(K_(p))=(1/2m_(e)v_(e)^(2))/(1/2m_(p)v_(p)^2)`
` :. (v_(e))/(v_(p)) =sqrt((m_(p)K_(e))/(m_(e)K_(p)))`
` = sqrt((1.67xx10^(-27))/(9.11xx10^(-31))xx(10xx1.6xx10^(-19))/(100xx1.6xx10^(-19)))`
` =sqrt((16.7)/(9.11)xx10^(2))`
= `13.5`
`(v_(e))/(v_(p))gt1` so electron is faster .