Final answer:
The transition from level 8 to level 2 (8→2) of an electron corresponds to the shortest photon wavelength because it involves the greatest energy difference between those levels, which results in a photon with higher energy and shorter wavelength.
Step-by-step explanation:
The electron transition that corresponds to the shortest photon wavelength is determined by the energy difference between the two energy levels involved in the transition. According to the Rydberg formula, the energy of the emitted or absorbed photon during an electron transition is inversely proportional to the square of the wavelength, which implies that a greater energy difference results in a shorter wavelength. The transition from a higher energy level to a lower one (emission) releases a photon, while the opposite (absorption) requires a photon.
Out of the given transitions, the shortest wavelength corresponds to the transition with the largest energy difference. Since the energy levels of an atom (like hydrogen) are closer together as they get farther from the nucleus, the largest energy difference would be between the two levels farthest apart. Therefore, the transition from level 8 to level 2 (8→2) would involve the highest energy difference and consequently produce the shortest wavelength of photon.
The wavelength is related to the other properties of the photon such as its frequency and energy. The shorter the wavelength, the higher the frequency and the more energy the photon carries. Understanding such properties is fundamental in the study of atomic and quantum physics, including the behavior and characteristics of elements such as hydrogen.