How much work is needed to assemble an atomic nucleus containing three protons such as Be) if we model it as equilateral triangle of side 2.0*10^-15 m with a proton at each vertex? Assume the protons started very far away.

3.456 * 10⁻⁴³ J

Explanation:

The work done in bringing two charges q₁ and q₂ separated by a distance, r together is W = kq₁q₂/r. With the first charge q₁ in place, the work done in bringing the second charge into the vertex of the equilateral at a distance, r is W₁₂ = kq₁q₂/r. Since the first and second charges are in place, the work done in bringing the third charge q₃ in place is work done W₁₃ between q₁ and q₃ = kq₁q₃/r plus work done W₂₃ between q₂ and q₃ = kq₂q₃/r. So the total work done in assembling the atomic nucleus is W = W₁₂ + W₁₃ + W₂₃ = kq₁q₂/r + kq₁q₃/r + kq₂q₃/r. Since q₁ = q₂ = q₃ = q = 1.6 * 10⁻¹⁹ C, W = 3kq²/r. Since r = side of equilateral triangle = 2.0 * 10⁻¹⁵ m. W = 3 * 9 * 10⁹ * (1.6 * 10⁻¹⁹) ²/2.0 * 10⁻¹⁵ = 3.456 * 10⁻⁴³ J ≅ 3.46 * 10⁻⁴³ J