question_answer 41)

  Deuterium was discovered in 1932 by Harold Urey by measuring the small change in wavelength for a particular transition in 1H and 2H. This is because, the wavelength of transition depend to a certain extent on the nuclear mass. If nuclear motion is taken into account, then the electrons and nucleus revolve around their common centre of mass. Such a system is equivalent to a single particle with a reduced mass (X, revolving around the nucleus at a distance equal to the electron-nucleus separation. Here where M is the nuclear mass and me is the electronic mass. Estimate the percentage difference in wavelength for the 1st line of the Lyman series in 1H and 2H. (Mass of 1H nucleus is 1.6725 x 10-27 kg, Mass of 2H nucleus is 3.3374 x 10-27 kg, Mass of electron = 9.109 x 10-31 kg).

Answer:

                  If we take into account the nuclear motion,  the stationary state energies will be given by                                 Let be reduced mass of hydrogen, and be reduced mass of deuterium (H2). The frequency of 1st line of Lyman series in hydrogen is given by  The percentage difference in wave number is AS me <<MH<MD =