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 = `1.67xxl0^-27kg`, `1 eV = 1.60 xx 10^-19 J`)

Explanation

mass of electron, `m_e = 9.11xx10^(-31) kg`, mass of proton,`m_p = 1.67xx10^(-27) kg `
velocity of electron = `v_e` velocity of proton = `v_p`.
The kinetic energy of electron `1/2 m_ev_e^2 = 10k ev " " ...(i)`
The kinetic energy of proton, `1/2 m_ev_p = 100k eV " " ....(ii)`
Dividing (i) by (it) we get `(1/2 m_ev_e^2)/(1/2 m_ev_p^2) = (10 xx 1.6 xx 10^(-16)J)/(100 xx 1.6 xx 10^(-16)J) implies (m_ev_e^2)/(m_p v_p^2) = 1/10`
or `(v_e)/(v_p) = sqrt(1/10 (m_p)/(m_e)) = sqrt(1.67 xx 10^(-27))/(10 xx 9.11 xx 10^(-31)) implies (v_e)/(v_p) = 13.54`
So, the electron moves faster than proton.