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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=4 orbit?

Asked in GUJCET 2021 · Postulates, radius, speed and angular momentum

• (1) 2.12×10⁻¹⁰ m
• (2) 8.48×10⁻¹⁰ m
• (3) 4.24×10⁻¹⁰ m
• (4) 10.6×10⁻¹⁰ m

Step-by-step solution

Why the other options are wrong

• (1) 2.12×10⁻¹⁰ m is 4×5.3×10⁻¹¹ m: it scales the radius by n instead of n².
• (3) No single slip gives 4.24×10⁻¹⁰ m, exactly half the answer. Sanity check: r₄=4²×5.3×10⁻¹¹ m=8.48×10⁻¹⁰ m.
• (4) No single slip gives 10.6×10⁻¹⁰ m, which is 20 times the innermost radius; for n=4 the factor is n²=16.

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