Question

A Van de Graaff generator produces a beam of 2.09-MeV deuterons, which are heavy hydrogen nuclei containing a proton and a neutron.

(a) If the beam current is 11.9 µA, how far apart are the deuterons?

Answer 1

Here we have given that,

A Van de Graaff generator produces a beam of 2.09-MeV deuterons

current = 11.9 µA,

Nor for the how far apart are the deuterons we have to go through as ,

energy of each particle with mass
m=2*1.6748 ×10^-27 kg

and

charge dq=1.602×10^-19 C will be here ,

E = 2.09 MeV = 2.09 ×10^6 * 1.602×10^-19 Joule =0.5m*v^2

So that

v=√(2E/m);
And the current is

I =dq/dt =dq*v/(v*dt) =dq*v/ds =11.9e-6 A,

hence distance in here will be

ds =dq*v/I

So lets substitute the values wil get,

ds = 1.602e-19 *√(2*2.09e6 * 1.602e-19/(2*1.6748e-27)) / 11.9e-6

ds = (190.34368513164) ×10^-9 m

ds = 190.3436 nm

Which is the distance between the deuterons.