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Question: In a hypothetical system, a particle of mass m and charge – 3q is moving around a very heavy particl...

In a hypothetical system, a particle of mass m and charge – 3q is moving around a very heavy particle charge q. Assume that Bohr's model is applicable to this system, then velocity of mass m in first orbit is-

A

3q22ε0h\frac{3q^{2}}{2\varepsilon_{0}h}

B

3q23ε0h\frac{3q^{2}}{3\varepsilon_{0}h}

C

3q2πε0h\frac{3q}{2\pi\varepsilon_{0}h}

D

3q4πε0h\frac{3q}{4\pi\varepsilon_{0}h}

Answer

3q22ε0h\frac{3q^{2}}{2\varepsilon_{0}h}

Explanation

Solution

mv2r\frac{mv^{2}}{r} = 3q24πε0r2\frac{3q^{2}}{4\pi\varepsilon_{0}r^{2}}

mvr = 3q24πε0V\frac{3q^{2}}{4\pi\varepsilon_{0}V} and, nh2π\frac{nh}{2\pi} = mvr

for n = 1

h2π\frac{h}{2\pi} = 3q24πεV\frac{3q^{2}}{4\pi\varepsilon V}

or v = 3q22ε0h\frac{3q^{2}}{2\varepsilon_{0}h}