Question

A proton has the initial speed of 5.1×105 m/s.

(a) what is the potential difference required to bring the protonto rest?

(b) what is the potential difference required to reduce the initialspeed by a factor of 2?

(c) what is the potential difference required to reduce the KE by afactor of 2?

Answer 1

a) Because the K.E. of the proton is changing to the P.E. So applying the conservation of energy

K.E. = P.E.

where V is the potential difference.

mass of the proton is 938 ,

where q = e is the charge of the proton and

So this much potential difference is required to stop the proton.

b) Again conservation of energy

Because final speed is half of the initial speed.

So this much potential difference is required to reduce the speed by a factor of 2.

c) conservation of energy

Because final K.E is half of the initial K.E.

So this much potential difference is required to reduce the proton's K.E by a factor os 2.