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Concepts Of Physics MCQ Edition [Volume 2]PhysicsBohr's Model and Physics of the Atom

In a one-electron system, the radius of the shortest orbit is given as 18 pm . This system could be

Options

  1. Adeuterium
  2. BLi ⁺⁺
  3. Chydrogen
  4. DHe ^+

Correct answer

B. Li ⁺⁺

Step-by-step solution

The radius of the n -th orbit for a hydrogen-like species is given by: r_n = 52.9 n^2 Z pm For the shortest orbit, n = 1 . Given that the radius is 18 pm , we can find the atomic number Z : 18 = 52.9 (1)^2 Z Z = 52.9 18 2.94 The closest integer value is Z = 3 , which corresponds to Lithium. Since it is a one-electron system, the species must be Li ⁺⁺ .

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