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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 2026 · Postulates, radius, speed and angular momentum

• (1) 1.59 × 10⁻¹⁰ m
• (2) 1.43 × 10⁻⁹ m
• (3) 1.06 × 10⁻¹⁰ m
• (4) 4.77 × 10⁻¹⁰ m

Step-by-step solution

Why the other options are wrong

• (1) 1.59×10⁻¹⁰ m is 3×5.3×10⁻¹¹ m: it scales the radius with n instead of n².
• (2) 1.43×10⁻⁹ m is 3³×5.3×10⁻¹¹ m: it cubes the quantum number where the Bohr radius needs its square.
• (3) 1.06×10⁻¹⁰ m is 2r₁, and nothing in the Bohr model doubles the radius at n=3; no single slip produces it. Sanity check: r₃=9r₁=4.77×10⁻¹⁰ m.

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