Question

A beam of monochromatic light is used to excite the electron in $Li ^{++}$from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x \times 10^{-10} m$. The value of $x$ is ________[Given $hc =1242\, eV\, nm$ ]

Answer 1

$Z=3$
$\frac{1}{\lambda}=R Z^{2}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)$
$n_{1}=1, n_{2}=3$,
$\frac{1}{\lambda}=R(9)\left(\frac{1}{1}-\frac{1}{9}\right)=8 R$
$\lambda=\frac{1}{8 R}=114 \times 10^{-10} m$