Deutrium was discovered in 1932 by Harold Urey by measuring the small change in wavelength for a particular transition in `.^(1)H` and `.^(2)H`. 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 `mu`, revolving around the nucleus at a distance equal to the electron -nucleus separation. Here `mu = 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 `.^(1)H` nucleus is `1.6725 xx 10^(-27)` kg, mass of `.^(2)H` nucleus is `3.3374 xx 10^(-27)` kg, Mass of electron `= 9.109 xx 10^(-31) kg`.)

Options

A. `8.1xx10^(-2)%`
B. `2.7xx10^(-2)%`
C. `0.81%`
D. `0.27%`

Answer

B