Answer
$r = 4.7\times 10^{-14}~m$
Work Step by Step
The Lithium atom has 3 protons
The Darmstadtium atom has 110 protons
We can express the kinetic energy in units of joules:
$K = (10.2~MeV)(\frac{1.6\times 10^{-19}~J}{1~eV}) = 1.632\times 10^{-12}~J$
To find the center-to-center distance when the Li nucleus stops, we can equate the potential energy with the initial kinetic energy:
$K = U$
$K = \frac{1}{4\pi~\epsilon_0}~\frac{q_1~q_2}{r}$
$r = \frac{1}{4\pi~\epsilon_0}~\frac{q_1~q_2}{K}$
$r = \frac{1}{(4\pi)~(8.854\times 10^{-12}~F/m)}~\frac{(3)(1.6\times 10^{-19}~C)(110)(1.6\times 10^{-19}~C)}{1.632\times 10^{-12}~J}$
$r = 4.7\times 10^{-14}~m$
