Q: 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 ?

Sol: Given, the radius of the innermost electron orbit of a hydrogen r_{1} = 5.3 × 10^{-11} m

As we know that r_{n} = n^{2} r_{1}

For n = 2, radius r_{2} = 2^{2} r_{1}

r_{2} = 4 × 5.3 × 10^(-11) = 2.12 × 10^{-10} m.

For n = 3, radius r_{3} = 3^{2} r_{1}

r_{3} = 9 × 5.3 × 10^{-11} = 4.77 × 10^{-10} m.