Question

Deuterium 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 $1.6725\times 10^{-27}kg$, Mass of ${}^{2}H$ nucleus is $3.3374\times 10^{-27}kg$, Mass of electron $=9.109\times 10^{-31}kg$.)

• A. $2.7\times 10^{-1}\%$
• B. $2.7\times 10^{-2}\%$
• C. $3.5\times 10^{-2}\%$
• D. $3.5\times 10^{-1}\%$

Answer 1

Answer: (B)

Correct answer is (b) $2.7\times 10^{-2}\%$