Question 24.100: An alpha particle (which has two protons) is sent directly t......

The distance r being looked for is that where the alpha particle has (momentarily) zero kinetic energy. Thus, energy conservation leads to

K_0+U_0=K+U \Rightarrow\left(0.48 \times 10^{-12} J \right)+\frac{(2 e)(92 e)}{4 \pi \varepsilon_0 r_0}=0+\frac{(2 e)(92 e)}{4 \pi \varepsilon_0 r} .

If we set r_0=\infty\left(\text { so } U_0=0\right) then we obtain r=8.8 \times 10^{-14} \,m .