Question 286: Work, Energy and Power & Circular Motion

Question

The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as $$U = {\alpha  \over {{r^{10}}}} - {\beta  \over {{r^5}}} - 3$$where, $$\alpha$$ and $$\beta$$ are positive constants. The equilibrium distance between two atoms will be $${\left( {{{2\alpha } \over \beta }} \right)^{{a \over b}}}$$, where a = ___________.

Accepted Answer

$$F =  - {{dU} \over {dr}}$$
$$F =  - \left[ { - {{10\alpha } \over {{r^{11}}}} + {{5\beta } \over {{r^6}}}} ight]$$
for equilibrium, F = 0
$${{10\alpha } \over {{r^{11}}}} = {{5\beta } \over {{r^6}}}$$
$${{2\alpha } \over \beta } = {r^5}$$
$$r = {\left( {{{2\alpha } \over \beta }} ight)^{1/5}}$$
$$ 	herefore $$ $$a = 1$$

Work, Energy and Power & Circular Motion

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