Question

A proton is located at a distance of 0.053 m from a point charge of +8.30 ?C. The repulsive electric force moves the proton until it is at a distance of 0.17 m from the charge. Suppose that the electric potential energy lost by the system were carried off by a photon. What would be its wavelength?? Answer is not 1.28e^-12 nm

Answer 1

given

Q = 8.3 micro C = 8.3*10^-6 C
d1 = 0.053 m
d2 = 0.17 m

we know for proton,
q = 1.6*10^-19 C
m = 1.67*10^-27 kg

let v is the speed of proton when it is at 0.17 m from Q.

Apply cosnervation of energy

k*Q*q/d2 + (1/2)*m*v^2 = k*Q*q/d1

9*10^9*8.3*10^-6*1.6*10^-19/0.17 + (1/2)*1.67*10^-19*v^2 = 9*10^9*8.3*10^-6*1.6*10^-19/0.053

v = 1363 m/s

wavelength of proton, lamda = h/(m*v)

= 6.626*10^-34/(1.67*10^-27*1363)

= 2.91*10^-10 m or 0.291 nm <<<<<<<-------------Answer