Question

Calculate the speed of a proton that is accelerated through a potential difference of 48 V to −8 V. The mass of the proton is mp = 1.67 × 10−27 kg, and its charge is qp = 1.60 × 10−19 C. The proton has an initial speed vi = 65 m/s.

Answer 1

The proton has the same electric charge as the electron, with an opposite sign (proton +, electron -).
Therefore, like the electron, a proton will gain 56 electron-volts of kinetic energy, which works out to 1.602×10^-19 J * 56 = 8.9712×10^-16 J.
Then, we know K. E. = mv^2 / 2, so v^2 = 2*K.E./m.
The mass of a proton is 1.673×10^-27 kg, giving us the figure v^2 = 1.0725×10^-12.
Taking the square root gives v = 1035600.6 m/s.
Since 56 has only 3 significant digits, we round our answer to 1035600.6 m/s.
Since this is so much less than the speed of light, relativistic effects can be ignored.