The radius of the innermost orbit of hydrogen atom is 5.3 × 10-11 m. The radii of n = 2 orbit is:

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  1. 1.06 × 10-10 m
  2. 2.12 × 10-10 m
  3. 10.6 × 10-10 m
  4. 21.2 × 10-10 m

Answer (Detailed Solution Below)

Option 2 : 2.12 × 10-10 m
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Given:

The radius of innermost orbit of a hydrogen atom \(r_0=5.3\times10^{-11}m\)

Let \(r_2 \) be the radius of the orbit at n=2.

Concept:

The radius of outermost orbit of a hydrogen atom is given as

  • \(r_{n}=n^2r_0\)

 

Explanation:

The radius in orbit n=2 can be find out as,

\(r_{n}=n^2r_0\)

\(r_2=(2)^2r_0\)

\(r_2=4\times5.3\times10^{-11}\)

\(r_2=21.2\times10^{-11}m=2.12\times10^{-10}m\)

Hence, the correct answer is Option-2- \(r_2=2.12\times10^{-10}m\).

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