Question

Calculate the energy of the emitted photon as well as the wavelength and frequency of electromagnetic radiation emitted from the hydrogen atom when the electron undergoes the transition from n = 5 to n = 1. In what region of the spectrum does this line occur?

Answer 1

RH = redberg's constant = 1.0973 x 10^7 m-1

1 / = R_H [1 / n1^2 - 1 / n2^2]

         = 1.0973 x 10^7 [1 / 1 - 1 /5^2]

         = 1.053 x 10^7 m-1

E = h C /

    = 6.625 x 10^-34 x 3 x 10^8 x 1.053 x 10^7

     = 2.09 x 10^-18 J

energy of the emitted photon = 2.09 x 10^-18 J

wavelength = 9.50 x 10^-8 m = 95 nm

frequency = C / = 3 x 10^8 / 9.50 x 10^-8 = 3.16 x 10^15 Hz