If A singly ionized xenon gas is used for an ion drive engin

If A singly ionized xenon gas is used for an ion drive engine, which has the ion pass through an accelerating voltage of 10 KV, how many atoms per second do I need to send out to get a thrust of 91 mN? (Hint: use F*dt=m*dv - comes from F=ma and a=dv/dt, Xe=131 AMU) #of atoms needed per second =?

Solution

use KE = PE

0.5 mv^2 = eV

spped v^2 = 2 eV/m

v^2 = (2*1.6*10^-19 * 10000)/(1.67*10^-27 * 131)

v = 1.21 *10^5 m/s

so F*dt = mdV

F dt = 131 * 1.67 *10^-27* 1.21*10^5

F dt = 2.64 *10^-15 Ns

so Number of atom per sec = 91*10^-3/(2.64 *10^-15)

dN/dt = 3.44 *10^13 atom/s