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If r is the interatomic distance, a and ...

If `r` is the interatomic distance, `a` and `b` are positive constants, `U` denotes potential energy which is a function dependent on `r` as follows :
`U=(a)/(r^(10) )-(b)/(r^(5))`.
The equilibrium distance between two atoms is

A

`((b)/(2a))^((1)/(5))`

B

`((2a)/(b))^((1)/(5))`

C

`((b)/(2a))^((1)/(10))`

D

`((2a)/(b))^((1)/(10))`

Text Solution

Verified by Experts

The correct Answer is:
B
`u= (a)/(r^(10))-(b)/(r^(5))`
`(du)/(dr)= (-10a)/(r^(11)) + (5b)/(r^(6))`
`(du)/(dr)`= zero for equilibrium
`therefore 0= (-10a)/(r^(11)) + (5b)/(r^(6))`
`therefore (2a)/(r^(5))=b therefore r^(5) = (2a)/(b)`
`therefore r= ((2a)/(b))^(1//5)`
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