The potential energy (U) of a diatomic molecule is a function dependent on r (inter atomic distance) as
$U = \frac{α}{r^{10}} - \frac{β}{r^{5}} - 3$
Where, $α$ and $β$ are positive constants. The equilibrium distance between two atoms will be ${(\frac{2 α}{β})}^{\frac{a}{b}},$ where $a =________$ .

Question

Infinity Learn · Accepted Answer

$$U=ar10$$−β$$r5$$−$$3At$$ equilibrium $$F=0$$⇒$$F=$$−$$dUdr=$$−−$$10$$α$$r11+5$$β$$r6$$−$$0$$⇒$$0=10$$α$$r11$$−$$5$$β$$r6$$⇒$$10$$α$$r11=5$$β$$r6$$⇒α$$=$$β$$2r5$$⇒$$2$$αβ$$=r5$$⇒$$r=2$$αβ$$1/5$$ So, $$a=1$$ and $$b=5$$

Equilibrium

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Equilibrium

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The potential energy (U) of a diatomic molecule is a function dependent on r (inter atomic distance) as U=αr10−βr5−3Where, α and β are positive constants. The equilibrium distance between two atoms will be 2αβab, where a=________.

U=ar10−βr5−3At equilibrium F=0⇒F=−dUdr=−−10αr11+5βr6−0⇒0=10αr11−5βr6⇒10αr11=5βr6⇒α=β2r5⇒2αβ=r5⇒r=2αβ1/5 So, a=1 and b=5

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