Question

Two particles, a proton with charge 1.6x10-19C and mass 1.67x10-27kg and an alpha particle with charge 3.2x10-19C and mass 6.64X10-27 kg are separated by an extremely large distance. They approach each other along a straight line with initial speed of 2.5x105 m/s each. Calculate the separation between the particles when they are closest to each other.

Answer 1

From the conservation of energy:

$$0.5(m+M)v^2=\frac{ke(2e)}{r}$$

$$0.5(1.67\cdot 10^{-27}+6.64\cdot 10^{-27})(2.5\cdot 10^5)^2\\=2\frac{9\cdot 10^{9}(1.6\cdot 10^{-19})^2}{r}$$

$$r=1.8\cdot 10^{-12}\ m$$