Question

Potential energy as a function of r is given by U =  `"A"/"r"^10-"B"/"r"^5`, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be ______.

Options

• `("A"/"B")^(1/5)`

• `("B"/"A")^(1/5)`

• `("2A"/"B")^(1/5)`

• `("B"/"2A")^(1/5)`

Answer 1

Potential energy as a function of r is given by U =  `"A"/"r"^10-"B"/"r"^5`, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be `underlinebb(("2A"/"B")^(1/5))`.

Explanation:

At equilibrium, `vec"F"=0`

⇒ `(-"du")/"dr"=0`

⇒ `(-"d")/"dr"("A"/"r"_10-"B"/"r"^5)=0`

⇒ `+"A"/"r"^11xx10-(5"B")/"r"^6=0`

⇒ `1/"r"^6[(10"A")/"r"^5-(5"B")/1]=0`

⇒ `(10"A")/"r"^5=5"B"`

⇒ `"r"^5 = (10"A")/(5"B")`

⇒ `"r" = ((2"A")/"B")^(1/5)`