The ratio of minimum to maximum wavelength of radiation that en electron in the gorund stsate can cause in a Bohr's hydrgen atom is:

Options

A. `1//2`
B. zero
C. `3//4`
D. `27//32`

Answer

C

Explanation

Energy of radiation that corresponds to the energy difference between two energy levels `n_(1)` and `n_(2)` is given as:
`E = 13.6 ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))eV` (numerically)
`E` is minimum when `n_(1) = 1` and `n_(2) = 2`
`E_(min) = 1.6 ((1)/(1) - (1)/(4))eV = 13.6 xx (3)/(4)eV`
`E` is maximum when `n_(1) = 1` and `n_(2) = oo`.
(The atom is ionized that is knows as ionization energy)
`E_(max.) = 13.6 (1-(1)/(oo)) = 13.6 eV`
`(E_(min))/(E_(max)) = (3)/(4)` or `(hc//lambda_(max))/(hc//lambda_(min)) = (3)/(4)`
`(lambda_(min))/(lambda_(max)) = (3)/(4)`