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Q.

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=________.

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answer is 1.

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Detailed Solution

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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