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?

Given, radius of innermost orbit, r₁ = 5.3 × 10^–11 m

Then, let r₂ be the radius of orbit at n = 2.

Then, r₂ = (n)²r₁

As shown in the diagram:

⇒ r₂ = 2² × 5.3 × 10^–11 m

⇒ r₂ = 2.12 × 10^–10 m

For n = 3, we have,

⇒ r₃ = (n)² r₁

⇒ r₃ = 3² × 5.3 × 10^–11 m

⇒ r₃ = 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