Suppose an electron is attracted towards the origin by a force k/r where k is a constant. By applying Bohr model, the radius r_n and kinetic energy T_ - Physics MCQ AIEEE 2026 | ExamTest.live

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Suppose an electron is attracted towards the origin by a force k / r where k is a constant. By applying Bohr model, the radius r_{n} and kinetic energy T_{n} of the n^{th} orbital are:

Solution & Step-by-step Explanation

Centripetal force = attractive force: \frac{m v ^{2}}{r} = \frac{k}{r} ⟹ m v^{2} = k .Kinetic energy T = \frac{1}{2} m v^{2} = \frac{k}{2} . Since k is constant, T_{n} is independent of n .Bohr's quantization: m v r = \frac{nh}{2 π} ⟹ r = \frac{nh}{2 πm v} .From m v^{2} = k, v is constant.Therefore, r \propto n .

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Suppose an electron is attracted towards the origin by a force k / r where k is a constant. By applying Bohr model, the radius r_{n} and kinetic energy T_{n} of the n^{th} orbital are:

T_{n} \propto 1/ n^{2}, r_{n} \propto n^{2}

T_{n} independent of n, r_{n} \propto n

T_{n} \propto 1/ n, r_{n} \propto n

T_{n} \propto 1/ n, r_{n} \propto n^{2}

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