Question

Using Bohr atom model, show that the radius of the first three orbits in

hydrogen atom are in the ratio 1 :4:9.

Answer 1

For Bohr's model, radius of nth orbit is represented as:
R_n = ε₀ n²h² / πme²
R₁ = ε₀ 1²h² / πme² ----------(1)
R₂ = ε₀ 2²h² / πme² ----------(2)
R3 = ε₀ 3²h² / πme² ----------(3)
Taking ratio R₁:R₂:R₃ = 1:4:9

Hence, the radius of the first three orbits in hydrogen atom are in the ratio 1 :4:9.