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R is the interatomic distance, a and b a...

R is the interatomic distance, a and b are positive constants, u denotes potential energy which is a function dependent on R as follows `v = 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) = (-10 a)/(r^11) + (5b)/(r^6)`
`(dU)/(dr) = `zero for equillibrium
`therefore 0 = (-10 a)/(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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