Question

How much work is necessary to bring the proton from rest infinetly far away to rest at a distance of 3m from the nucleus? I've know how to get the answer for the first part of the question which asks, " How much (mass) energy is released when a 13C nucleus combines with a proton?" which is 7.5505 MeV, but I'm not sure how to answer the energy question. I think you'd use the equation Wnc= Kf-Ki+ Uf+Ui but I don't know where to go from there. Can someone please explain/help me with this question?

Answer 1

See, if you want to bring the proton close to the nucleus, you need to do work on it because the nucleus would actually repel the proton.

So the work done will be change in potential energy

Initial potential energy at infinity will be zero

Final potential energy will be given by the formula kq₁q₂/r

q₁ = 1.6 × 10-¹⁹ q2 = 13 and r = 3

So final potential energy comes out to be 9× 10⁹ × 1.6 × 13× 10^-19/3

= 6.24 × 10^-9 J