Suppose in an imginary world the angular momentum is quantized to be even integral multiples of `h//2 pi`. What is the longest possible wavelenght emitted by hydrogen atoms in visible range in such a world according to Bohr's model?

Answer

D

Explanation

Even quantum numbers are allowed
`n_1=2`, `n_2=4`
For minimum energy or for longest possible wavelength.
`E=13.6((1)/(n_1^2)-(1)/(n_2^2))`
`=13.6[(1)/((2)^2)-(1)/((4)^2)]`
`=13.6 (1/4-1/16)`
`=(13.6 xx 12)/(64)=2.55`
i.e. `2.55 = (hc)/lambda`
`lambda = (hc)/(2.55) = 1242/2.55 nm`
`=487.05 nm = 487 nm`