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The orbital period of an electron in the first Bohr orbit of hydrogen is 1.52 × 10-16 s. What is its orbital period in the n = 3 orbit?

Answer: 4.10 × 10-15 s.

  • A 4.56 × 10-16 s
  • B 1.37 × 10-15 s
  • C 9.12 × 10-15 s
  • D 4.10 × 10-15 s

Correct answer: D. 4.10 × 10-15 s

Explanation: The Bohr orbital period varies as T proportional to n3. Therefore T3 = 33T1 = 27 × 1.52 × 10-16 = 4.10 × 10-15 s.

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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