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Question

Suppose that the potential energy of an hypothetical atom consisting of a proton and an electron by U=−ke2/3r3. Then if Bohr's postulates are applied to this atom, then the radius of the 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 B 1/n2
Given, Potential Energy (U)=Ke23r3
we Know
F=dudrF=ddr(Ke23r3)F=+Ke33(31r4)F=Ke2r4
Now, it is given it follow Bohr's postalate F= centripetal force =mv2r
mv2r=ke2r4mv2=ke2r3(i)
By. conservation of angular momentum mvr=nh2πvαnr(ii)
from (i) and (ii) n2r2α1r3 or, rα1n2

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