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

Step-by-step solution

As the hydrogen atoms emit radiation of six different wavelengths, some of them must have been excited to n = 4 , The energy in n = 4 state is E 4 = E 1 4 2 = - 1 3 · 6 e V 1 6 = - 0 · 8 5 eV. The energy needed to take a hydrogen atom from its ground state to n = 4 is 13 .6 eV - 0 .85 eV = 12 .75 eV . The photons of the incident radiation should have 12.75 eV of energy. So hc λ = 1 2 · 7 5 eV or , λ = hc 1 2 · 7 5 eV = 1 2 4 2 eV nm 1 2 · 7 5 eV = 97 .5 nm .