I first approached this problem with the idea that I could try to find the temperature of the HII region given that we already know the background temperature. Still, I am stuck on finding the region's temperature.
A second approach was to try to find if the cloud is optically thick, which...
From my understanding, you can equate ψ1(x) and ψ2(x) at the boundary of x = a, so I plugged in the values of a into x for both equations and I got ψ1(x) = 0 and ψ2(x) = ## (a-d)^2-c ##. I am a bit stuck on where to go from here.
Oh my bad. All of the values in Bohr's radius are constants if I am not mistaken. ##a_0 = \frac {4\pi\varepsilon_0\hbar^2} {m_e*e}##. 4, \pi, \hbar and the permittivity are all constants. An electron's rest mass is constant (##0.511 Mev##), and the elementary charge of an electron is also a...