A proton has an initial speed of 4.0 x 10 ^5 m/s A) What potential difference is

Question

A proton has an initial speed of 4.0 x 10 ^5 m/s
A) What potential difference is required to bring the protonto rest?
B) what potential difference is required to reduce the initialspeed of the proton by a factor of 2?
C) What potential difference is required to reduce the initialkinetic energy of the proton by a factor of 2?
A) What potential difference is required to bring the protonto rest?
B) what potential difference is required to reduce the initialspeed of the proton by a factor of 2?
C) What potential difference is required to reduce the initialkinetic energy of the proton by a factor of 2?

Explanation / Answer

Initial speed of the proton vi =4*105 m/s mass of the proton m = 1.673*10-27 kg charge of proton e = 1.6*10-19 C a) According to law of conservation of energy1/2mvi 2 = e(vf -vi )                                            = eV         (vf = 0 )                       V = mvi2/2e               substitute  the values to get solution. b) Final speed of the proton = vi/2 =2*105 m/s from the above we have V = 1/2mvi2 - 1/2 m(vi/2)2 /e                            =     mvi2 /2e(1-1/4)                                                                                                                                                    = mvi2 /2e (3/4 ) substitute the values to get solution c) Given KE reduces to half the initial value      kf = ki/2    1/2 mvi2+eVi    =1/2mvf2+eVf       ki - ki /2 = eV    V = ki /2e 1/2mvi 2 /2e = mvi2 /4e substitute the values to get solution   

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