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An electron is pulled toward the origin by a central force of magnitude k/r, where k is a constant and r is the electron’s distance from the origin. If the Bohr model is used for this system, the radius of the nth orbit is rₙ and the electron’s kinetic energy is Tₙ. Which statement is correct?

1. Tₙ varies as 1/n², and rₙ varies as n²
2. Tₙ does not depend on n, and rₙ varies as n
3. Tₙ varies inversely with rₙ, and rₙ varies as n
4. Tₙ varies inversely with rₙ, and rₙ varies as n²

Correct answer: Tₙ does not depend on n, and rₙ varies as n

Solution

For F = k/r, mv^2/r = k/r gives mv^2 = k (constant), so kinetic energy T_n = k/2 is independent of n. Bohr quantization mvr = n*hbar then gives r_n ∝ n.

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