The potential energy (U) of a diatomic molecule is a function dep… - Vidyadip

MCQ

The potential energy $(U)$ of a diatomic molecule is a function dependent on $r$ (interatomic distance) as

$U =\frac{\alpha}{ r ^{10}}-\frac{\beta}{ r ^{5}}-3$

where, $\alpha$ and $\beta$ are positive constants. The equilibrium distance between two atoms will be $\left(\frac{2 \alpha}{\beta}\right)^{\frac{a}{b}},$ where a $=$ ..........

A
$2$
✓
$1$
C
$3$
D
$0$

✓

Answer

Correct option: B.

$1$

b
For equilibrium

$\frac{ dU }{ dr }=0$

$\frac{-10 \alpha}{r^{11}}+\frac{5 \beta}{r^{6}}=0$

$\frac{5 \beta}{r^{6}}=\frac{10 \alpha}{r^{11}}$

$r ^{3}=\frac{2 \alpha}{\beta}$

$r=\left(\frac{2 \alpha}{\beta}\right)^{\frac{1}{3}}$

$a=1$

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