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Question

In a hypothetical system of particles a mass m with charge 3q is moving around a very heavy particle having charge q. Assuming Bohr’s model to be true to this system, the orbital velocity of mass m when it is nearest to heavy particle is

A
3q22ε0h
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B
3q24ε0h
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C
3q2ε0h
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D
4q2ε0h
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Solution

The correct option is A 3q22ε0h
As we know that centripetal force is provided by Coulomb's force, so
mv2r=3q34πϵ0r2
mvr=3q24πϵ0v.......(i)
and we know that
nh2π=mvr......(ii)

Using Bohr's (i) and (ii) and putting n=1
h2π=3q24πϵ0v
v=3q22πϵ0h

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