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?

The radius of the innermost orbit of a hydrogen atom, r1 = 5.3 x 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

= 4 x 5.3 x 10⁻¹¹ = 2.12 x 10⁻¹⁰ m

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

r3 = (n)²r1

= 9 x 5.3 x 10⁻¹¹=4.77 x 10⁻¹⁰ m

Hence, the radii of an electron for n = 2 and n = 3 orbits are 22.12 x 10⁻¹⁰ m and 4.77 x 10⁻¹⁰ m respectively.