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NTA Abhyas JEE Main2020PhysicsAtomic PhysicsPractice

Which among the following has a Hydrogen-like spectrum and whose lines have wavelengths four times shorter than those of atomic Hydrogen?

Options

  1. AHelium ion
  2. BBeryllium ion
  3. CLithium ion
  4. DNone of these

Correct answer

A. Helium ion

Step-by-step solution

For Hydrogen like atom, 1 λ ' = R ⁡ Z ⁡ 2 1 n 1 2 - 1 n 2 2 ...(i) For Hydrogen atom, 1 λ = R ⁡ 1 n 1 2 - 1 n 2 2 ...(ii) Dividing Eqn (ii) by Eqn (i), we get λ ' λ = R ⁡ 1 n 1 2 - 1 n 2 2 RZ 2 1 n 1 2 - 1 n 2 2 or λ ' λ = 1 Z ⁡ 2 According to problem, λ ' = λ 4 ∴ λ ' 4 λ ' = 1 Z ⁡ 2 ∴ Z = 2 The atomic number of Helium atom is 2 . Hence, the required element is Helium.

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