Question

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.

Answer 1

Answer:

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