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STANDARDPhysics-Atomic Structure

STANDARD Physics Bohr Model MCQ Question

Type: MCQ-conceptual-Medium-Class 11

The relation between the orbital radius and the electron velocity for a dynamically stable orbit in a hydrogen atom is (where, all notations have their usual meanings)

A

v = e24πε0mr\frac{e^2}{4\pi\varepsilon_0mr}

B

r = e24πε0v\frac{e^2}{4\pi\varepsilon_0v}

C

v = 4πε0me2r\frac{4\pi\varepsilon_0}{me^2r}

D

r = ve24πε0m\frac{v e^2}{4\pi\varepsilon_0m}

Correct Answer

Option A

Detailed Explanation

In a hydrogen atom, the electrostatic force of attraction between the revolving electrons and the nucleus provides the requisite centripetal force to keep them in their orbits. Thus, Fe=FcF_e = F_c, leading to the relation v=e24πε0mrv = \frac{e^2}{4\pi\varepsilon_0mr}.

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