An alpha particle is a nucleus of helium It has twice the ch

An alpha particle is a nucleus of helium. It has twice the charge and four times the mass of the proton. When they were very far away from each other, but headed toward directly each other, a proton and an alpha particle each had an initial speed of 0.005c, where c is the speed of light. What is their distance of closest approach? Hint: There are two conserved quantities. Make use of both of them. (c = 3.00 × 108 m/s, k = 1/40 = 8.99 × 109 N m2/C2, e = 1.60 × 10-19 C, mproton = 1.67 x 10-27 kg) (Give your answer to the nearest 0.001 pico meters (10-12 m)

Solution

THis is a conservative field here the kinetic energy will get stored as the potential energy of the system. And the closest distance of approah will be when the speed becmes zero

KE = PE

1/2m v^2 + 1/2 4m v^2 = k e * 2e/R

9.39 * 10-15 = 46 *10-29/R

R = 4.9 * 10-14 = 49 fm