JEE Main 2022 · 25 June · morning · Single correct · +4 / −1

The ratio for the speed of the electron in the 3ʳᵈ orbit of He⁺ to the speed of the electron in the 3ʳᵈ orbit of hydrogen atom will be :

  1. (a) 1 : 1
  2. (b) 1 : 2
  3. (c) 4 : 1
  4. (d) 2 : 1
Answer and solution

Answer (d) 2 : 1

Solution

Physics sir · 3 steps

In Bohr's model the orbit speed goes as Z over n, so with the same n only Z matters.

  1. Bohr speed formula. For a hydrogen-like atom, the electron speed in the nth orbit is proportional to the nuclear charge number Z and inversely proportional to n.

    vₙ = (Z e²)/(2 ε₀ n h) = 2.19 × 10⁶ Z/n m s⁻¹

  2. Same orbit. Both electrons are in the orbit with n = 3, so n cancels in the ratio. What is left is v_(He⁺)/v_H = Z_(He)/Z_H = 2/1.
  3. So. The electron in He⁺ moves twice as fast, and the ratio is 2 : 1, option (d).

The idea to keep. Remember the Bohr scalings: speed goes as Z/n, radius as n²/Z, energy as Z²/n². Write the ratio first and let the common factors 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 2022.