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Question

Suppose that the potential energy of an hypothetical atom consisting of a proton and an electron is given by U=−ke2/3r3. Then if Bohr's postulates are applied to this atom, then the radius of the nt orbit will be proportional to:-

A
n2
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B
1/n2
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C
n3
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D
1/n3
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Solution

The correct option is D 1/n3
Given, (potential Energy) =ke23r3 we know relation between force and potential Energy
F=dydrF=ddr(Ke23r3)F=Ke2r4
If Bohr's postulate is true for this Force = centripital force =mv2r
So, mv2r=ke2r4(i)
and from Bohr's postulate angular momentum (mvr)=nh2π
mvr=nh2π(ii)
Putting value of v from (ii) in (i)
m(nh2πmr)2r=ke2r4
n2h24π2mr=ke2r4
r α 1n2

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