An electron and a proton are detected in a cosmic ray experiment, the first with kinetic energy 10 keV and second with 100keV. Which is faster, the electron or proton ? Obtain the ratio of their speeds. Take mass of electron `9.11xx10^(-31)kg`. Mass of proton `=1.67xx10^(-27)kg` and `1eV=1.6xx10^(-19)J.`

Explanation

`E_(1)=(1)/(2)m_(e)v_(e)^(2)=10xx1.6xx10^(-16)` …(i)
`E_(2)=(1)/(2)m_(p)v_(p)^(2)=100xx1.6xx10^(-16)` …(ii)
Divide (i) by (ii) `(m_(e)v_(e)^(2))/(m_(p)v_(p)^(2))=(1)/(10)`
`(v_(e))/(v_(p))=sqrt((1)/(10)(m_(p))/(m_(e)))=sqrt((1.67xx10^(-27))/(10xx9.11xx10^(-31)))=10^(2)sqrt((1.67)/(91.1))=13.53`