AIIMS2019Physics-Atomic Physics

AIIMS 2019 Physics Bohr Model MCQ Question

Type: MCQ-numerical-Medium-Class 12

In hydrogen atom, the electron is moving round the nucleus with velocity 2.18×106 m/s2.18 \times 10^6\text{ m/s} in an orbit of radius 0.528 A˚0.528\text{ \AA}. The acceleration of the electron is

A

9×1018 m/s29 \times 10^{18}\text{ m/s}^2

B

9×1022 m/s29 \times 10^{22}\text{ m/s}^2

C

9×1022 m/s29 \times 10^{-22}\text{ m/s}^2

D

9×1012 m/s29 \times 10^{12}\text{ m/s}^2

Correct Answer

Option A

Detailed Explanation

The expression for the acceleration of an electron, given by a=v2ra = \frac{v^2}{r}, calculates to a=(2.18×106m/s)20.528×1010ma = \frac{(2.18 \times 10^6 \, \text{m/s})^2}{0.528 \times 10^{-10} \, \text{m}}, which simplifies to approximately 9×1022m/s29 \times 10^{22} \, \text{m/s}^2. This result aligns with option (A), confirming it as the correct answer. The other options (B, C, and D) provide lower values, which do not accurately reflect the calculations based on the given velocity and radius, demonstrating a misunderstanding of the relationship between velocity, radius, and acceleration in circular motion.

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