Solution The key idea here is that throughout the scattering process,
the total mechanical energy of the system consisting of an a-particle
and a gold nucleus is conserved The system’s initial mechanical
energy is Ei, before the particle and nucleus interact, and it is equal
to its mechanical energy Ef when the a-particle momentarily stops The initial energy Ei is just the kinetic energy K of the incoming
a- particle The final energy Ef is just the electric potential energy U
of the system