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IAT IISER2026ChemistryStructure of Atom

What is the ratio of the velocity of an electron in the fourth orbit of Be ³⁺ to the velocity of the electron in the second orbit of He ^+ ?

Options

  1. A1:1
  2. B1:2
  3. C6:1
  4. D3:2

Correct answer

A. 1:1

Step-by-step solution

The velocity of an electron in the n -th orbit of a hydrogen-like ion is given by v Z n . For Be ³⁺ , Z = 4 and n = 4 . v_ Be ³⁺ 4 4 = 1 For He ⁺ , Z = 2 and n = 2 . v_ He ⁺ 2 2 = 1 The ratio of their velocities is v_ Be ³⁺ v_ He ⁺ = 1 1 = 1:1 . Answer: 1:1

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