Final answer:
The hydrogen Balmer lines are strongest in the spectra of medium-temperature stars because at this temperature, a significant number of hydrogen atoms are excited to the second energy level. In hot stars, more highly excited atoms occupy higher energy levels, leading to a decrease in the number of atoms in the second energy level. In cool stars, the majority of hydrogen atoms are in the ground state and can only absorb high-energy photons, which are scarce in the radiation from cool stars.
Step-by-step explanation:
The hydrogen Balmer lines are strongest in the spectra of medium-temperature stars because at this temperature (around 10,000 K), a significant number of hydrogen atoms are excited to the second energy level. These excited atoms can then absorb additional photons, rise to higher levels of excitation, and produce a dark absorption line. However, in very hot stars with temperatures above 25,000 K, and in very cool stars with temperatures below 3500 K, the hydrogen Balmer lines are weak or essentially nonexistent.
Hot stars have a higher temperature, which means that more atoms are highly excited and occupy higher energy levels. As a result, the number of atoms in the second energy level, required to produce the Balmer lines, decreases. On the other hand, cool stars have most of their hydrogen atoms in the ground state (unexcited) and can only absorb photons with sufficient energy to lift them to higher energy levels. Since these high-energy photons lie in the ultraviolet part of the electromagnetic spectrum, which is scarce in radiation from cool stars, the Balmer lines appear weak or absent.
Overall, the strength of the hydrogen Balmer lines in stellar spectra depends on the temperature of the star, with medium-temperature stars being optimal for producing visible hydrogen lines.