Question

Radius of third Bohr orbit is 0.477 nm. Calculate the radius of the second Bohr orbit.

Answer 1

Given: Radius of 3^rd orbit, r₃ = 0.477 nm = 0.477 × 10⁻⁹ m

To find: Radius of 2^nd orbit, r² = ?

We know, r_n ∝ n²

Radius of 2^nd orbit n = 2 and for 3^rd orbit n = 3

∴ `r_2/r_3 = (2)^2/(3)^2 = 4/9`

∴ `r_2 = r_3 xx 4/9`

= `0.477 xx 10^-9 xx 4/9`

= 0.212 × 10⁻⁹ m

r₂ = 0.212 nm

r₂ = 2.12 Å