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)`
`therefore v_(e)=sqrt((2(K.E.)_(e))/(m_(e)))=sqrt((2xx10xx10^(3)xx1.6xx10^(-19))/(9.1xx10^(-31)))`
`v_(e)=5.93xx10^(7)ms^(-1)`
Similarly `v_(p)=sqrt((2xx100xx10^(3)xx1.6xx10^(-19))/(1.67xx10^(-29)))=0.438xx10^(7)ms^(-1)`
Hence `(v_(e))/(v_(p))=(5.93xx10^(7))/(0.438xx10^(7))=13.54`
or `v_(e):v_(p)::27:2`
or `v_(e):v_(p)::14:1` (approximately)