An alpha particle is the nucleus of a He-4 atom and has a rest mass of 3727.38 MeV/c2. How much energy is required to accelerate an alpha particle from rest to 0.6c? What is the momentum of the alpha particle once it reaches this speed? Would more, less or the same amount of energy be required to accelerate a proton from rest to this speed
An alpha particle is the nucleus of a He-4 atom and has a rest mass of 3727.38 MeV/c2. How much energy is required to accelerate an alpha particle from rest to 0.6c? What is the momentum of the alpha particle once it reaches this speed? Would more, less or the same amount of energy be required to accelerate a proton from rest to this speed?
The relativistic kinetic energy of the particle is given by
Where mo = rest mass of particle, c = Speed of light in vacuum, v = Speed of particle
The total relativistic energy of the particle is given by
Where p = momentum of the particle
Also, 
Rest mass of alpha particle is 
= 3727.38 MeV/c2
Initial speed of the alpha particle is vi = o m/s (at rest)
At initial speed relativistic gamma factor is given by
Thus initial kinetic energy of the particle is
Final speed of the alpha particle is vf = 0.6 c
At final speed relativistic gamma factor is given by
Thus final kinetic energy of the particle is
Therefore energy required to accelerate alpha particle from rest to 0.6c is equal to change in kinetic energy of the alpha particle. Thus
Final total energy of the alpha particle is
Let pf = final momentum of the alpha particle
Thus
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