AIIMS 2019 Physics Energy Levels MCQ Question

To determine the energy transfer to a H⁻-like atom when it is excited from the ground state (n = 1) to n = 3, we use the formula for the energy levels of a hydrogen-like atom: $E_n = -\frac{Z^2 \cdot 13.6 \, \text{eV}}{n^2}$. For H⁻ (where Z = 1), the energy levels are $E_1 = -13.6 \, \text{eV}$ and $E_3 = -\frac{13.6}{9} \, \text{eV}$, resulting in an energy difference of $\Delta E = E_3 - E_1 = -\frac{13.6}{9} + 13.6 = 12.1 \, \text{eV}$.

Options B (10.2 eV), C (12.75 eV), and D (10 eV) are incorrect because they do not correspond to the calculated energy difference between the specified energy levels for a H⁻-like atom.