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The radius of the n^ th Bohr orbit of a Be ³⁺ ion is equal to the radius of the first Bohr orbit of a hydrogen atom. What is the value of n ?

Options

  1. A2
  2. B1
  3. C3
  4. D4

Correct answer

A. 2

Step-by-step solution

The radius of the n^ th Bohr orbit of a hydrogen-like species is given by: r_n = a₀ n^2 Z For a Be ³⁺ ion, the atomic number Z = 4 . Therefore, the radius of its n^ th orbit is: r_n = a₀ n^2 4 The radius of the first Bohr orbit of a hydrogen atom ( Z = 1, n = 1 ) is a₀ . According to the given condition: a₀ n^2 4 = a₀ n^2 4 = 1 n^2 = 4 n = 2 Answer: 2

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