a proton is moving at a speed of 0.900 times the velocity of lifght.find its kinetic energy in joules and MeV

Question

a sum related to atomic physics.......eV(electron volt)

Answer 1

A speed of 0.900c is close enough to the speed of light that you must use the relativistic equation for kinetic energy.  The classical equation

 

K = mv²/2

 

will not work at such a high speed.  Use

 

K = m₀c² [(1 - v²/c²)^-1/2 - 1]

 

m₀ = rest mass of proton = 1.67 x 10^-27 kg = 938 MeV/c²

c = speed of light = 3 x 10⁸ m/s

v = 0.900c  [given]

 

Plug in the numbers.  To get the answer in joules, work with mass in kg and c in m/s.  To get the answer in MeV, work with mass in MeV/c².