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According to Bohr's theory, the radius of electron in an orbit described by principal quantum number n and atomic number Z is proportional to:
1. Z2n2
2. Z2 / n2
3. Z2 / n
4. n2 / Z

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Correct Answer - Option 4 : n2 / Z

Concept:

  •  Bohr’s theory: He proposed that the electrons orbited in a specific orbit with a fixed radius of shells, with a fixed radius.
    • According to Bohr's model, the electron would absorb energy in the form of photons to get excited to a higher energy level.
    • It derives a radius for the nth excited state of hydrogen-like atoms.

The radius of Bohr's orbit

 \(Z = \frac{{{n^2}{h^2}}}{{4{\pi ^2}m{e^2}}} \times \frac{1}{Z}\)

Where n = principal quantum number of orbit, Z = atomic number, h = Plank’s constant, m = Mass of electron, e = elementary charge

Explanation:

  • From the above discussion, it is clear that the r is directly proportional to n2.

From Bohr’s relation, r ∝ n2

So the correct option is n2 / Z.

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