The radius of the innermost electron orbit of a hydrogen atom is 5.3 �

1.	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 m = 3 orbits?
Answer» Given r₁ = 5.3 × 10^-11m n₁ = 1, n₂ = 2, r₂ = ? n₃ = 3, r₃ = ? Since r ∝ n² ∴ r₁ ∝ n₁² And r₂ ∝ n₂² ∴ \(\frac{r_2}{r_1}=\frac{n^2_2}{n_1^2}\) = \(\frac{2^2}{1}=\frac{4}{1}\) or r₂ = 4 × r₁ = 4 × 5.3 × 10^-11 or e₂ = 2.12 × 10^-10m Also r₃ ∝ n₃² \(\frac{r_3}{r_1}=\frac{n^2_3}{n_1^2}\)= \(\frac{3^2}{1}=\frac{9}{1}\) or r₃ = 9r₁ = 9 × 5.3 × 10^-11 or r₃ = 4.77 × 10^-10m.

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 m = 3 orbits?

Answer»

Given r₁ = 5.3 × 10^-11m
n₁ = 1, n₂ = 2, r₂ = ?
n₃ = 3, r₃ = ?
Since r ∝ n²
∴ r₁ ∝ n₁²
And r₂ ∝ n₂²

∴ \(\frac{r_2}{r_1}=\frac{n^2_2}{n_1^2}\) = \(\frac{2^2}{1}=\frac{4}{1}\)

or r₂ = 4 × r₁ = 4 × 5.3 × 10^-11
or e₂ = 2.12 × 10^-10m
Also r₃ ∝ n₃²

\(\frac{r_3}{r_1}=\frac{n^2_3}{n_1^2}\)= \(\frac{3^2}{1}=\frac{9}{1}\)

or r₃ = 9r₁ = 9 × 5.3 × 10^-11
or r₃ = 4.77 × 10^-10m.