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

Question

Physics

Trey Barnett

2 February, 02:36

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

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Jaiden Schaefer · Answer 1

Potential energy of system of three protons kept on the vertices of an equilateral triangle of side 2 x 10⁻¹⁵ m

= k (q₁q₂ / r₁₂ + q₂q₃/r₂₃ + q₁q₃ / r₁₃)

= k x 3 q² / r

= 9 x 10⁹ x 3 x (1.6 x 10⁻¹⁹) ² / 2 x 10⁻¹⁵

= 34.56 x 10⁻¹⁴ J

Potential at infinity is zero

so work done

= 34.56 x 10⁻¹⁴ J - 0

= 34.56 x 10⁻¹⁴ J