Question
The wavelengths involved in the spectrum of deuterium $$\left( {_1^2D} \right)$$ are slightly different from that of hydrogen spectrum, because
A.
the size of the two nuclei are different
B.
the nuclear forces are different in the two cases
C.
the masses of the two nuclei are different
D.
the atraction between the electron and the nucleus is
differernt in the two cases
Answer :
the masses of the two nuclei are different
Solution :
The wavelength of spectrum is given by
$$\frac{1}{\lambda } = {Rz^2}\left( {\frac{1}{{n_1^2}} - \frac{1}{{n_2^2}}} \right)\,\,\,\,\,\,{\text{where}}\,R = \frac{{1.097 \times {{10}^7}}}{{1 + \frac{m}{M}}}$$
where $$m$$ = mass of electron
$$M$$ = mass of nucleus.
For different $$M, R$$ is different and therefore $$\lambda $$ is different