The interatomic forces between two atoms varies as under:

$straight F subscript alt proportional to negative straight alpha over straight r to the power of 6 space space space space and space space space space straight F subscript rep proportional to negative straight b over straight r to the power of 9$

Find the equilibrium separation between two atoms.

Solution

The net force between two atoms is

straight F equals straight F subscript alt plus straight F subscript rep equals negative straight alpha over straight r to the power of 6 plus straight b over straight r to the power of 9

Let r₀ be the equilibrium separation between the two atoms. At equilibrium separation the net force between the two atoms is zero.

therefore space space space space space space space space minus straight alpha over straight r subscript 0 to the power of 6 plus straight b over straight r subscript 0 to the power of 9 equals 0 rightwards double arrow space space space space space space space space space space straight r subscript 0 cubed equals straight b over straight a rightwards double arrow space space space space space space space space space straight r subscript 0 equals cube root of straight b over straight a end root

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