(a) Find the electric potential difference ΔVe required to stop an electron (called a "stopping potential") moving with an initial speed of 1.93 107 m/s.
(b) Would a proton traveling at the same speed require a greater or lesser magnitude of electric potential difference?
(c) Find a symbolic expression for the ratio of the proton stopping potential and the electron stopping potential, ΔVp/ΔVe. (Use the following as necessary: mp for the mass of proton and me for the mass of electron.)
Thie problem can be solved using the conservation of energy.
Kf - Ki + Uf - Ui = 0
And so Kf - Ki = - (Uf - Ui)
Substitute in the proper equations now:
0 - (1/2)*m*v^2 = - (q*V)
where q = -1.602*10^-19 C
m = 9.109*10^31 kg
v = 1.93*10^7 m/s
Now just substitute in these values and solve for V.
V = - ((1/2)*(9.109*10^31 kg)*(1.93*10^7 m/s)^2) / (1.602*10^-19 C))
and so V = -1060 V or -1.06 kV
For Part B, the answer is greater because a proton has greater mass (mass proton = 1.673*10^-27 kg) and hence would require a greater change of electric potential.
For Part C, the ratio is simply = - (mass of proton)/ (mass of electron)
or: - mp / me