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(A) For a system following Bohr's model,the electrostatic force provides the necessary centripetal force: $\frac{1}{4\pi\varepsilon_0} \frac{(3q)(q)}{

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$\frac{3q^2}{2\varepsilon_0 h}$

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(A) For a system following Bohr's model,the electrostatic force provides the necessary centripetal force: $\frac{1}{4\pi\varepsilon_0} \frac{(3q)(q)}{r^2} = \frac{mv^2}{r} \implies \frac{3q^2}{4\pi\varepsilon_0 r} = mv^2$  .......$(1)$According to Bohr's quantization condition for the ground state $(n=1)$: $mvr = \frac{h}{2\pi} \implies r = \frac{h}{2\pi mv}$  .......$(2)$Substitute $r$ from $(2)$ into $(1)$:$\frac{3q^2}{4\pi\varepsilon_0} \left( \frac{2\pi mv}{h} \right) = mv^2$$\frac{3q^2}{2\varepsilon_0 h} = v$Thus,the orbital velocity is $v = \frac{3q^2}{2\varepsilon_0 h}$.

In a hypothetical system,a particle of mass $m$ and charge $-3q$ is moving around a very heavy particle having charge $q$. Assuming Bohr's model to be true for this system,the orbital velocity of mass $m$ when it is nearest to the heavy particle is:

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