Physics - Modern Physics Question with Solution | TestHub

In a hypothetical hydrogen atom the electrostatic potential energy of interaction of proton and electron is given by $\mathrm{U}={\mathrm{U}}_0\ell \mathrm{n}\left(\frac{\mathrm{r}}{{\mathrm{r}}_0}\right)$ where ${\mathrm{U}}_0$ and ${\mathrm{r}}_0$ are constants and r is radius of circular orbit of electron. For such hydrogen atom the energy difference between ${\mathrm{n}}^{\text{th }}$ and ${\mathrm{m}}^{\text{th }}$ state is represented by $\Delta {\mathrm{E}}_{\text{nm }}$. Calculate the ratio $\Delta {\mathrm{E}}_{12}:\Delta {\mathrm{E}}_{24}$. Assume Bohr's assumption of angular momentum quantization to hold.