IGNOU PHE 13 2026 - The potential energy of the Neon crystal is described by the expressio

Question

The potential energy of the Neon crystal is described by the expression:

$$U(r) = -4\varepsilon \left[ \left( \frac{\rho_0}{r} \right)^6 - \left( \frac{\rho_0}{r} \right)^{12} \right]$

29 Jan 2026

Answer :

Word Count : 219

The potential energy of the Neon crystal is given by [ U(r) = -4 \varepsilon \left[ \left( \frac{\rho_0}{r} \right)^6 - \left( \frac{\rho_0}{r} \right)^{12} \right]. ] To find the equilibrium separation (r_0), we set the derivative of (U(r)) with respect to (r) equal to zero: [ \frac{dU}{dr} = 0. ] Differentiating: [ \frac{dU}{dr} = -4 \varepsilon \left[ -6 \frac{\rho_0^6}{r^7} + 12 \frac{\rho_0^{12}}{r^{13}} \right] = 0. ] Simplify: [ -6 \frac{\rho_0^6}{r^7} + 12 \frac{\rho_0^{12}}{r^{13}} = 0 ] [ 12

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