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If potential energy between an electron and a proton in an hydrogen atom is given by U=Ke23r3 then radius r  of an orbit is proportional to principal quantum number n as

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a
n0
b
n-1
c
n2
d
n-2

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detailed solution

Correct option is D

F=-dUdr=-ddrke23r3=ke2r4 =mv2r     v2=ke2mr3 again from Bohr hypothesis mvr =nh2πv2=n2h24π2m2r2=ke2mr3r= 4π2me2kn2h2


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