Question

How much work is needed to assemble an atomic nucleus containing three protons (such as Be) if we model it as an equilateral triangle of side 2.00×10−15m with a proton at each vertex? Assume the protons started from very far away.

Answer 1

Answer:

2.16 MeV

Explanation:

To determine the amount of work done that is needed to assemble the atomic mass; we need to apply the equation;

U = $\frac{3}{4 \pi E_o} (\frac{e^2}{r})$

where:

$\frac{1}{4 \pi E_o}$ = proportionality constant = $(9*10^9N.m^2/C^2)$

e = magnitude of the charge of each electron = $(1.6*10^{-19} C)^2$

r = length of each side of the vertex = $(2.00*10^{-15}m)$

So; replacing our values into above equation; we have:

U = $3\frac{(9*10^9N.m^2/C^2)(1.6*10^{-19} C)^2}{(2.00*10^{-15}m)}$

U = 3.456 × 10 ⁻¹³ J

If we have to convert our unit from J to Mev; then we are going to have:

U = 3.456 × 10 ⁻¹³ J $(\frac{1 MeV}{1.602*10^{-13}J})$

U = 2.16 MeV

Therefore, the amount of work done needed to assemble an atomic nucleus =  2.16 MeV