For hydrogen atom electron in n th Bohr orbit, the ratio of the radius of orbit to its de-Broglie wavelength is

Step-by-step solution

For n th Bohr orbit, r = ε 0 n 2 h 2 π m Z e 2 de-Broglie wavelength λ = h m v The ratio of both r and λ ,   r λ = ε 0 n 2 h 2 π m Z e 2 × m v h = ε 0 n 2 h v π Z e 2 But v = Z e 2 2 h ε 0 n for n th orbit Hence, r λ = n 2 π