Question

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?

Answer 1

The radius of the innermost orbit of a hydrogen atom, r₁ = 5.3 × 10⁻¹¹ m

Let r₂ be the radius of the orbit at n = 2. It is related to the radius of the innermost orbit as:

r₂ = (n)²r₁

= (2)² × 5.3 × 10⁻¹¹

= 4 × 5.3 × 10⁻¹¹

= 2.12 × 10⁻¹⁰ m

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

r₃ = (n)²r₁

= (3)² × 5.3 × 10⁻¹¹

= 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.