Question

Which of the following relation gives the potential energy of a diatomic molecule?

• A. \(U(r)=-\dfrac{a}{r^m}+\dfrac{b}{r^n}\)
• B. \(U(r)=ar^m-br^n\)
• C. \(U(r)=ar^m+br^n\)
• D. \(U(r)=ar^m-\dfrac{b}{r^n}\)

Hint:

Diatomic molecular potential has a negative attractive term and a positive repulsive term.

Answer 1

The Correct Option is A

Concept:
The potential energy of a diatomic molecule contains two parts: \[ \text{Attractive potential energy} \] and \[ \text{Repulsive potential energy} \]

Step 1: Attractive part.
At larger interatomic distance, atoms attract each other. The attractive part is negative: \[ -\frac{a}{r^m} \]

Step 2: Repulsive part.
At very small interatomic distance, electron cloud repulsion becomes strong. The repulsive part is positive: \[ +\frac{b}{r^n} \]

Step 3: Combine both parts. \[ U(r)=-\frac{a}{r^m}+\frac{b}{r^n} \] \[ \therefore \text{Correct Answer is (A)} \]