Monochromatic radiation of wavelength `lambda` is incident on a hydrogen sample in ground state hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelength .Find the value of `lambda`

Explanation

As the hydrogen atoms emit radiation of six difference wavelength some of then must have been excited to `n = 4` The energy `n = 4` state is
`E_(0) = (E_(1))/(4^(2)) = - (13.6eV)/(16) = - 0.85eV`
Theenergy needed to take a hydrogen atom from its ground stateto `n = 4` is
`13.6eV - 0.85eV = 12.75eV`
The photons of the incident rediation have `12.75eV` of energy So
`(hc)/(lambda) = 12.75eV`
`or, `lambda= (hc)/(12.75eV)`
`= (1242evnm)/(12.75eV) = 97.5nm`