The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as U=(α /r10)-(β /r5)-3 Where, a and b are positive constants. The equilibrium distance between two atoms will ((2 α /β ))(a/b)⋅ Where a=

Question

The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as U=(α /r10)-(β /r5)-3 Where, a and b are positive constants. The equilibrium distance between two atoms will ((2 α /β ))(a/b)⋅ Where a= (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

F=-(d U/d r) F=-[- (10 α /r11) + (5 β /r6)] for equilibrium, F=0 (10 α /r11)=(5 β /r6) (2 α /β )=r5 r=((2 α /β ))1 / 5 a=1

Q. The potential energy (U) of a diatomic molecule is a function dependent on r (interatomic distance) as U=r10α​−r5β​−3 Where, a and b are positive constants. The equilibrium distance between two atoms will (β2α​)ba​⋅ Where a=

F=−drdU​ F=−[−r1110α​+r65β​] for equilibrium, F=0 r1110α​=r65β​ β2α​=r5 r=(β2α​)1/5 a=1

$F = - \frac{d U}{d r}$
$F = - [- \frac{10 α}{r ^{11}} + \frac{5 β}{r ^{6}}]$
for equilibrium, $F = 0$
$\frac{10 α}{r ^{11}} = \frac{5 β}{r ^{6}}$
$\frac{2 α}{β} = r^{5}$
$r = (\frac{2 α}{β})^{1/5}$
$a = 1$