In an electric propulsion system, alpha particles are accelerated through a potential difference of 100kV at an average rate of 10^20 alpha particles per second. Calculate the average thrust the system can provide.

Take the mass of alpha particle to be 6.6410^-27 kg accurate to 3 s.f. Note that the the work done in an electric field accross a potential difference is E = QV, where Q is the total charge of the alpha particle and V is the potential difference. Recall that an alpha particle consists of two protons and two neutrons, each proton has a charge of +1.610^-19C and the neutrons zero charge, which means the charge on the alpha particle is 3.210^-19C. E = QV = 3.210^-19 * 100,000 = 3.210^-14J of kinetic energy gained per alpha particle. E = 0.5mv^2 = (mv)^2/2m = p^2/2m = > p = sqrt(2mE) where p is the momentum gained per alpha particle with kinetic energy E and mass m, note that this equation applies if the speed of the alpha particle is much less than the speed of light- which is true in this case. p = sqrt(2 6.6410^-27 * 3.210^-14 ) = 2.061... * 10^-20 so the momentum gained is 2.061... *10^-20kgms^-1, given it started from rest. By Newton's second law of motion, force is equal to the rate of change of momentum, i.e. F = dp/dt. Since 10^20 particles are accelerated each second the total force is 10^20 multiplied by the force experienced by each particle. F = 2.061... * 10^-20 * 10^20 = 2.06N 3 s.f. By Newton's third law the thrust provided would therefore be 2.06N accurate to 3 s.f. Note that it's a good habit to not use rounded intermediary values in the calculations as this carries on rounding error, instead use the memory of the calculator to carry on the actual values. Also, round the final answer to the lowest degree of accuracy used in the data given in the question.