A Level Physics Practice Exam

Why are different frequencies of photons released when electrons in hydrogen atoms transition from the n = 3 energy level?

1. Electrons always return to the ground state directly

2. Electrons return to lower levels via various paths

3. Only a single frequency of photon is emitted

4. Higher energy levels do not emit any photons

The correct answer is: Electrons return to lower levels via various paths

The reasoning behind the answer lies in understanding the nature of electron transitions between energy levels in an atom. When electrons in hydrogen (or any atom) transition from a higher energy level, such as n = 3, to lower energy levels, they do not have to drop directly to the ground state (n = 1). Instead, electrons can take various paths, moving from n = 3 to n = 2 and then from n = 2 to n = 1, for example. Each transition corresponds to a specific energy difference, which, according to the equation \( E = hf \) (where \( E \) is the energy of the emitted photon, \( h \) is Planck's constant, and \( f \) is the frequency), results in the emission of photons with different frequencies. When an electron transitions between levels, the energy difference varies depending on the specific transition path taken. Consequently, the emission of different frequencies of photons can be attributed to these various paths that electrons may follow as they return to lower energy states, rather than a singular frequency or a direct drop to the ground state. This contributes to the characteristic spectral lines seen in the emission spectrum of hydrogen, each corresponding to a unique transition between energy