The ground (n=1) state of hydrogen atom is acutally 2 different quantum states with slightly different energies. Because of a magnetic interaction between the proton and electron, the quantum state where the proton and electron spins are aligned has an energy a few microelectronvolts above the energy of the state where the spins are anti-alligned.
A) If the hydrogen atoms undergoes a transition between these states, it emits a photon with a characteristic wavelength of 21 cm. (astronomers can detect such photons with a radio telescope and thus determine the distribution of hydrogen gas in the sky). What is the energy difference between the 2 states.
B) if a hydrgen cloud in intergalactive space has a temperature of about 2.9K (about equal to the temerature of the cosmic background radiation). about what fraction of hydrogen atoms in the N=1 level will be in the aligned state( and thus be capable of emitting the 21-cm photons)?