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The radius of the innermost electron orbit of a hydrogen atom is 5.3 × 10^{−11} m. What are the radii of the n = 2 and n = 3 orbits?

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#### Solution

The radius of the innermost orbit of a hydrogen atom, r_{1} = 5.3 × 10^{−11} m.

Let r_{2} be the radius of the orbit at n = 2. It is related to the radius of the innermost orbit as:

`"r"_2 = ("n")^2 "r"_1`

= 4 × 5.3 × 10^{−11}

= 2.12 × 10^{−10} m

For n = 3, we can write the corresponding electron radius as:

`"r"_3 = ("n")^2 "r"_1`

= 9 × 5.3 × 10^{−11}

= 4.77 × 10^{−10} m

Hence, the radii of an electron for n = 2 and n = 3 orbits are 2.12 × 10^{−10} m and 4.77 × 10^{−10 }m respectively.

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