Which of the following wavelengths lying in the range 500 nm to 700 nm is in hydrogen spectrum?

Step-by-step solution

The energy of a photon of wavelength 500 nm is hc λ = 1 2 4 2 eV nm 5 0 0 nm = 2 · 4 4 eV. The energy of a photon of wavelength 700 nm is hc λ = 1 2 4 2 eV nm 7 0 0 nm = 1 · 7 7 eV. The energy difference between the states involved in the transition should, therefore, be between 1.77 eV and 2.44 eV. Figures above diagram shows some of the energies of hydrogen states. It is clear that only those trasitions which end at n = 2 may emit photons of energy between 1.77 eV and 2.44 eV. Out of these only n = 3 → n = 2 fall