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The radius of the innermost electron orbit of a hydrogen atom is 5.3×10⁻¹¹ m. What is the radius of the n=3 orbit?

Asked in GUJCET 2022 · Postulates, radius, speed and angular momentum

• (1) 4.12×10⁻¹⁰ m
• (2) 4.77×10⁻¹⁰ m
• (3) 2.12×10⁻¹⁰ m
• (4) 2.24×10⁻¹⁰ m

Step-by-step solution

Why the other options are wrong

• (1) comes from no single slip produces 4.12×10⁻¹⁰ m. Sanity check: r₃=3²×5.3×10⁻¹¹=4.77×10⁻¹⁰ m.
• (3) 2.12×10⁻¹⁰ m is the radius of the n=2 orbit, 2²×5.3×10⁻¹¹ m, not of n=3.
• (4) comes from no single slip produces 2.24×10⁻¹⁰ m. Sanity check: r∝ n² gives 9×5.3×10⁻¹¹=4.77×10⁻¹⁰ m for n=3.

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