Deuterium was discovered in 1932 by Harold Urey by measuring the small change in wavelength for a particular transition in 1 H 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 center of mass. Such a system is equivalent to a single particle with a reduced mass μ, revolving around the nucleus at a distance equal to the electron-nucleus separation. Here μ = m e M/ (m e + M) where M is the nuclear mass and m e is the electronic mass. Estimate the percentage difference in wavelength for the 1st line of the Lyman series in 1 H and 2 H. (Mass of 1H nucleus is 1.6725 × 10 –27 kg, Mass of 2 H nucleus is 3.3374 × 10 –27 kg, Mass of electron = 9.109 × 10 -31 kg.)

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 center of mass. Such a system is equivalent to a single particle with a reduced mass μ, revolving around the nucleus at a distance equal to the electron-nucleus separation. Here μ = m_eM/ (m_e + M) where M is the nuclear mass and m_e 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 × 10^–27 kg, Mass of ²H nucleus is 3.3374 × 10^–27 kg, Mass of electron = 9.109 × 10^-31 kg.)

For first Lyman series, we have,

∴

∴ for hydrogen,

------(1)

And for deuterium,

------(2)

Dividing 1 by 2 we get,

Now we know that,

and

∴

Now taking common from numerator, we get,

By binomial expansion we get,

∴

Now putting the values respectively, we get,

∴

1