JEE Main 2020 · 5 September · morning · Single correct · +4 / −1

The difference between the radii of 3ʳᵈ and 4ᵗʰ
orbits of Li²⁺ is R₁ . The difference between the
radii of 3ʳᵈ and 4ᵗʰ orbits of He⁺ is ΔR₂ .
Ratio ΔR₁ : ΔR₂ is :

  1. (a) 8 : 3
  2. (b) 3 : 2
  3. (c) 2 : 3
  4. (d) 3 : 8
Answer and solution

Answer (c) 2 : 3

Solution

Chemistry ma’am · 3 steps

Same two orbits in both ions, so only Z changes, and the radius goes as 1 over Z.

  1. Bohr radius formula. For a one-electron species, the radius of the nth orbit is rₙ = 0.529 n²/Z Å. A bigger nuclear charge pulls the orbit in closer.

    Δ R = r₄ - r₃ = 0.529×(4² - 3²)/Z = 0.529×7/Z Å

  2. Plug in each Z. Li²⁺ has Z = 3, so Δ R₁ = 0.529 × 7/3. He⁺ has Z = 2, so Δ R₂ = 0.529 × 7/2.
  3. So. Δ R₁ : Δ R₂ = 1/3 : 1/2 = 2 : 3, which is option (c).

The idea to keep. For the same pair of orbits in two hydrogen-like ions, everything cancels except Z. Radii go as n²/Z, so the higher Z ion has the smaller gap.

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

Study Atomic Structure

Asked about 170 times in JEE Main since 2020. This question is from 2020.