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The ratio of radius for second and third orbit of hydrogen atom is ________.

Asked in GUJCET 2024 · Postulates, radius, speed and angular momentum

• (1) 3 : 2
• (2) 2 : 3
• (3) 9 : 4
• (4) 4 : 9

Step-by-step solution

Why the other options are wrong

• (1) 3 : 2 is the ratio of the orbital speeds, v₂ : v₃, since vₙ∝1/n: it answers with the speeds instead of the radii, and the speeds fall as the orbit grows where the radii rise.
• (2) 2 : 3 is only the ratio of the quantum numbers, as if rₙ∝ n; the Bohr radius goes as n², so the squares are needed.
• (3) 9 : 4 is the same ratio upside down, r₃ : r₂; the question asks for second orbit to third.

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