Question

Astronomers use the line emission from the quantum state n = 3 to n = 2 to probe ionized hydrogen gas – that is, hydrogen gas stripped of its electron. In ionization equilibrium, a balance is established between the process of ionization and its reverse, recombination, in which a free electron e − and proton p recombine to form neutral atomic hydrogen H, releasing one or more photons γ : e − + p ↔ H + γ

The recombination generally puts the electron into an excited state, such as n = 3, from which it must transition downward to reach the ground state. These transitions are the source of the photons. The series of transitions n → 2 are historically known as the Balmer series, and labelled by the Greek letters (eg, n = 5 → 2 is Balmer-γ, often written H-γ, n = 4 → 2 is H-β. etc.) n = 3 → 2 is H-α.

a. What is the energy of a H-α photon according to the Bohr model? Give your answer in eV

b. What is the wavelength of a H-α photon? In which portion of the electromagnetic spectrum does this photon lie?

c. Roughly what temperature, in Kelvin, is required to excite H-α emission? Argue that the mean thermal energy kT must be approximately equal to the energy of a H-α photon.

Answer 1