JEE Main 2023 · 31 January · evening · Single correct · +4 / −1

The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

  1. (a) 2.25R
  2. (b) 3 R
  3. (c) R/3
  4. (d) 9 R
Answer and solution

Answer (a) 2.25R

Solution

Physics sir · 3 steps

Bohr radii grow as n squared, so compare 3² with 2² and the answer drops out.

  1. Radius rule. In Bohr's model the orbit radius is rₙ = a₀ n²/Z. For the same atom, a₀ and Z stay fixed, so rₙ ∝ n².

    r₃/r₂ = 3²/2² = 9/4 = 2.25

  2. Use the given radius. The second orbit has radius r₂ = R. So r₃ = 2.25 × R.
  3. So. The third orbit has radius 2.25R, which is option (a).

The idea to keep. In a Bohr atom the radius goes as n², speed as 1/n and energy as 1/n². For any orbit-to-orbit comparison, set up the ratio and the constants cancel.

Answer from the NTA final answer key. Solution by PrepWiser.

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Asked about 110 times in JEE Main since 2020. This question is from 2023.