Answer
$r = 1.3\times 10^{-13}~m$
Work Step by Step
A lithium atom has 3 protons
A thorium atom has 90 protons
We can express the kinetic energy in units of joules:
$K = (3.00~MeV)(\frac{1.6\times 10^{-19}~J}{1~eV}) = 4.8\times 10^{-13}~J$
To find the least center-to-center separation, we can equate the final potential energy with the initial kinetic energy:
$K = U$
$K = \frac{1}{4\pi~\epsilon_0}~\frac{q_1~q_2}{r}$
$r = \frac{1}{4\pi~\epsilon_0}~\frac{q_1~q_2}{K}$
$r = \frac{1}{(4\pi)~(8.854\times 10^{-12}~F/m)}~\frac{(3)(1.6\times 10^{-19}~C)(90)(1.6\times 10^{-19}~C)}{4.8\times 10^{-13}~J}$
$r = 1.3\times 10^{-13}~m$
