If potential energy function for the force between two atoms in a diatomic molecule is approximately given by U x = a x 8 - b x 4 , 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 m 8 and b = 20 J m 4 ]

Step-by-step solution

U ( x ) = 4 x 8 - 20 x 4 ∴ d U d x = 0 ⇒ - 8 × 4 x 9 + 20 × 4 x 5 ⇒ 4 x 5 20 - 8 x 4 = 0 x = ∞ and x 4 = 8 20 Also d 2 U d x 2 = + v e a t x 4 = 8 20 ∴ U m i n = 4 x 4 1 x 4 - 5 = 4 × 20 8 20 8 - 5 ⇒ U m i n = - 4 × 20 8 × 20 8 = - 25 J ∴ Dissociation energy = U i n f i n i t e - U m i n = 25 J