Q39 / 92 · NTA Abhyas (JEE Main) 2020 · Physics · Work Power Energy

If potential energy function for the force between two atoms in a diatomic molecule is approximately given by Ux=ax8-bx4, where a and b are constants in standard SI units and x is in metres. Find the dissociation energy of the molecule (in J). [Take a=4 J m8 and b=20 J m4]

Correct answer: 25

Solution

U(x)=4x8-20x4
∴ dUdx=0  ⇒  -8×4x9+20×4x5
⇒  4x520-8x4=0
x=∞ and x4=820
Also d2Udx2=+ve  at  x4=820
∴  Umin=4x41x4-5=4×208208-5
⇒  Umin=-4×208×208=-25  J
∴ Dissociation energy =Uinfinite-Umin=25 J

Hence, the correct answer is 25.

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