⚛️ Physics · Atoms · NEET & JEE

The de Broglie wavelength of an electron in the third Bohr orbit of hydrogen is approximately what value? Take the Bohr radius a0 = 0.529 × 10-10 m.

Answer: 9.97 10 -10 m.

A 9.97 × 10-10 m
B 6.28 × 10-10 m
C 3.32 × 10-10 m
D 1.59 × 10-9 m

Correct answer: A. 9.97 × 10-10 m

Explanation: The standing-wave condition is 2πr = nλ. For n = 3, r = 9a0, so λ = 2π(9a0)/3 = 6πa0 = 9.97 × 10-10 m.

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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The de Broglie wavelength of an electron in the third Bohr orbit of hydrogen is approximately what value? Take the Bohr radius a<sub>0</sub> = 0.529 &times; 10<sup>-10</sup> m.

Concept context

More Atoms questions

The de Broglie wavelength of an electron in the third Bohr orbit of hydrogen is approximately what value? Take the Bohr radius a<sub>0</sub> = 0.529 × 10<sup>-10</sup> m.