40 The following particles are each accelerated from rest through the same potential difference.
Which one completes the acceleration with the greatest momentum?
A ?-particle
B electron
C neutron
D proton
please explain. Its from ON07 QP1
All these particles will be accelarated in the same potential difference
the alpha particle has a charge of +2, the elecctron -1, the neutron 0 and the proton +1.
The Alpha particle will have the greatest force acting on it
Then the electron, then the proton.
Momentum = mass x velocity
Immediatelty ignore the neutron and electron. The neurton will not accelerate because it has no charge, so no velocity. The electron has negligble mass, so negligble momentum.
F=ma
Compare the proton and The Alpha particle
Proton has a force of 1 and The Alpha particle has a force of 2 on them, relative to each other
The mass of the proton is 1 and the mass of The Alpha particle is 4, relative to each other.
acceleration of the proton is 1 and the acc of The Alpha particle is 0.5
NOw we know that the velocity of the proton will increase faster than The Alpha particle
The both start from rest so using V=u+at, velocity = the acceleration x time
Momentum of the alpha particle = 4 x 0.5t = 2t
Momentum of the proton = 1 x 1t = t
Relative to each other, the momentum of the alpha particle increases by twice the momentum of the proton in 1 second.
This is a quantitative way of looking at it. But in the exam, I knew that the velocity of the alpha particle was only slightly smaller than the proton, and the alpha particle had 4 times the mass of the proton. I could confidently guess that the alpha particle would have the higher momentum.
