Question

A proton moves from a location where V =75 V to a spot whereV = -20 V.

(a) What is the change in the proton's kinetic energy?

(b) If we replace a proton with an electron, what is the change in kinetic energy?

Answer 1

Given that :

initial potential energy, V₁ = 75 V

final potential energy, V₂ = - 20 V

(a) the change in the proton's kinetic energy which is given as ::

K.E_p = - q V                                       { eq.1 }

where, V = V₂ - V₁

q = charge on proton = +1.6 x 10^-19 C

then   K.E_p = - q (V₂ - V₁)                                           { eq.2 }

inserting the values in eq.2,

K.E_p = - (+1.6 x 10^-19 C) [(- 20 V) - (75 V)]

K.E_p = - (1.6 x 10^-19 C) (- 95 V)

K.E_p = 152 x 10^-19 J

or   K.E_p = 1.52 x 10^-17 J

(increase in kinetic enegy)

(b) If we replace a proton with an electron, then its change in kinetic energy is given as ::

using eq.2,    K.E_e = - q (V₂ - V₁)    

where, q = charge on electron = -1.6 x 10^-19 C

inserting the values in eq.2,

K.E_e = - (-1.6 x 10^-19 C) [(- 20 V) - (75 V)]

K.E_e = (1.6 x 10^-19 C) (- 95 V)

K.E_e = -152 x 10^-19 J

or   K.E_e = - 1.52 x 10^-17 J

(decrease in kinetic energy)