JEE Physics 2023 Question with Solution

Given: An incident electron has energy $12.5 \, \text{eV}$ and bombards gaseous hydrogen.

Find: The number of spectral lines emitted.

For hydrogen, excitation from $n=1$ to $n=2$ requires $10.2 \, \text{eV}$ and excitation from $n=1$ to $n=3$ requires $12.09 \, \text{eV}$. Since the incident electron energy is $12.5 \, \text{eV}$, the atom can be excited up to a maximum of $n=3$.

The number of possible spectral lines emitted when de-excitation can occur among levels up to $n=3$ is

$$\frac{3(3-1)}{2}=3$$

Thus, the number of spectral lines emitted is $3$. Therefore, the correct option is C.