Deuterium was discovered in 1932 by Harold Urey by measuring the small change in wavelength for a particular transition in and . This is because the wavelength of transition depends 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 , revolving around the nucleus at a distance equal to the electron-nucleus separation. Here where is the nuclear mass and is the electronic mass. Estimate the percentage difference in wavelength for the 1 st line of the Lyman series in and . (Mass of nucleus is , Mass of nucleus is , Mass of electron kg.)

contexto.120

3 years ago

The energy of an electron in the nth state is given by the expression,

For hydrogen atom we have,

For deuterium atom we have,

The wavelength of the transition for hydrogen can be calculated as,

The wavelength of the transition for deuterium can be calculated as,

The difference between the wavelength can be calculated as,