A $12.5 \mathrm{~eV}$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

The energy of an electron in an excited state of hydrogen is given by the equation: <br/><br/> Code snippet<br/><br/> $E = -13.6 \frac{1}{n^2} \mathrm{~eV}$<br/><br/> where n is the principal quantum number of the state. <br/><br/> The energy of the electron beam is 12.5 eV, which is enough to excite the electron to the n = 3 state.<br/><br/> The possible transitions from n = 3 to lower energy states are: <br/><br/> n = 3 to n = 2, with a wavelength of 656.33 nm (H-alpha)<br/><br/> n = 3 to n = 1, with a wavelength of 102.57 nm (Lyman-alpha)<br/><br/> n = 2 to n = 1, with a wavelength of 121.57 nm (Lyman-beta)<br/><br/> Therefore, there are 3 possible spectral lines that can be emitted.