a charged particle beam is created using 16O nuclei physics

a charged particle beam is created using 16O nuclei physics. the beam has a steady current of 7.35 uA past a fixed point in space. As the beam travels along it spreads out due to forces between the nuclei. If on average two nuclei are seperated by 20.0 * 10^-10m, what is the magnitude of the force between them? What total charge moves past the point in 15.0 min. How many carbon nuclei move past the point in 1 hr.

Solution

the force between the two nuclei is,

     F = kq^2/r^2

        = (9x10^9)(8*1.6x10^-19)^2 / (20.0 * 10^-10)^2

        = 3.6864x10^-9 N

Current is, I = 7.35X10^-6 A, so the charge is,

      q = I*t = 7.35X10^-6 A * (15*60 s) = 6.6e-3 C = 6.6 mC

formula:

   activity : dN/dt = lambda*N

Here, N = number of atoms.

formula: N = N0e^-lambda*t

here,     lambda = ln2/T_1/2 and t = 1 hr , T1/2 = half life of carbon

use the above information to find the number of carbon atoms