For an electron in the nth Bohr orbit of hydrogen, how does its orbital period T vary with n?

For an electron in the nth Bohr orbit of hydrogen, how does its…

Answer: T is proportional to n 3.

A T is proportional to n
B T is proportional to n3
C T is proportional to n2
D T is proportional to 1/n

Correct answer: B. T is proportional to n3

Explanation: In the Bohr model, r is proportional to n2 and v is proportional to 1/n. Since T = 2πr/v, T is proportional to n3.

Comparison of the Thomson model and the Rutherford model of the atom: in the Thomson plum pudding model alpha particles pass almost straight through a diffuse positive sphere, while in the Rutherford model a concentrated central nucleus deflects some alpha particles through large angles, with the lower panels showing the alpha particle source and gold foil and the observed result of wide-angle scattering

The Geiger–Marsden alpha-scattering result: a few alpha particles bounce back at large angles, which rules out Thomson’s diffuse model and demands a tiny, massive, positively charged nucleus. Image: Kurzon, CC BY 3.0, via Wikimedia Commons.

Concept context

Thomson's plum-pudding model, Rutherford's nuclear model from alpha-scattering, Bohr's postulates and hydrogen spectrum, spectral series (Lyman to Pfund), Rydberg formula, and limitations of each model.

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For an electron in the nth Bohr orbit of hydrogen, how does its orbital period T vary with n?

Concept context

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