Question

The size of the nucleus is about 10^-14 m in diameter. If you wanted to add another proton to a Uranium nucleus (92 protons and 146 neutrons), how strong is the repulsive force at the "edge" of the nucleus?

Answer 1

Size of Uranium nuceus, \(d=10^{-14} \mathrm{~m}\)

Radius of the nucleus, \(r=5 \times 10^{-15} \mathrm{~m}\)

Charge of proton, \(q=1.6 \times 10^{-19} \mathrm{C}\)

Number of protons, \(n=92\) protons

$$ \begin{aligned} \text { Electrostatic force, } F &=\frac{k q_{1} q_{2}}{r^{2}} \\ &=\frac{n k q^{2}}{r^{2}} \\ &=\frac{92 \times 9 \times 10^{9} \times\left(1.6 \times 10^{-19}\right)^{2}}{\left(5 \times 10^{-15}\right)^{2}} \\ &=847.87 \mathrm{~N} \end{aligned} $$