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AIEEE 2004

JEE Main 2004 Chemistry question on Atomic Structure

Which hydrogen like species will have same radius as that of Bohr orbit of hydrogen atom?
  1. A.
    n=2,Li2+n = 2, \text{Li}^{2+}
  2. B.
    n=2,Be3+n = 2, \text{Be}^{3+}
  3. C.
    n=2,He+n = 2, \text{He}^+
  4. D.
    n=3,Li2+n = 3, \text{Li}^{2+}
Show answer and solution

Correct option: B

Solution

The Bohr orbit radius formula is r = (n²/Z) × a₀. For hydrogen's first Bohr orbit (n=1, Z=1), r = a₀. Setting n²/Z = 1, we need n² = Z. For Be³⁺, Z = 4, and with n = 2: n²/Z = 4/4 = 1, which equals the hydrogen Bohr radius. This is the only option satisfying n² = Z.

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