Q 12-12-090JEE MainJEE Main 2022 (27 Jun, Shift 1)Medium
A beam of monochromatic light is used to excite the electron in $\text{Li}^{++}$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x\times10^{-10}$ m. The value of $x$ is ______ .
[Given $hc = 1242$ eV nm]
Numerical value type. Enter your answer.
Answer: 114
For $\text{Li}^{++}$, $Z = 3$:
$$\Delta E = 13.6\,Z^2\left(1 - \frac19\right) = 13.6\times9\times\frac89 = 108.8\ \text{eV}$$
$$\lambda = \frac{hc}{\Delta E} = \frac{1242}{108.8}\ \text{nm} \approx 11.4\ \text{nm} = 114\times10^{-10}\ \text{m}$$
So $x \approx 114$.
Solution by Sreeraj P, M.Sc Physics