Question

At what speed will the momentum of a proton (mass 1 u) equal that of an alpha particle (mass 4 u) moving at 0.60 c ? answer in terms of v/c

Answer 1

we know,

relativistic momentum, P = mo*v/sqrt(1 - (v/c)^2)

mo ---> rest mass
v --> speed of the particle
c --> speed of light

let
mo1 = 4 u
v1 = 0.6*c

mo2 = u
v2 = ?

P_proton = P_alfa

mo2*v2/sqrt(1 - (v2/c)^2) = mo1*v1/sqrt(1 - (v1/c)^2)

u*v2/sqrt(1 - (v2/c)^2) = 4*u*0.6*c/sqrt(1 - 0.6^2)

v2/sqrt(1 - (v2/c)^2) = 3*c

v2/(3*c) = sqrt(1 - (v2/c)^2

(v2/(3*c))^2 = 1 - (v2/c)^2

on solving the above equation we get

v2 = 0.948*c <<<<<<<<<<------------------------Answer