# How to determine the temperature of a star according to the strength of the line in the spectra?

Based on the comments, I have changed some things.

Below is a graph showing the relative strength of $$H_\gamma$$ and Fe I lines of two stars. Which star is hotter?

This is a question from the book:An Introduction to Stellar Astrophysics(2010).Francis Leblanc. The full question is shown below. And also, some of my ideas:

1. As for Fe I, based on Saha equation, we can calculate as follows: $$\frac{n_{\mathrm{II}}}{n_{\mathrm{I}}}=\frac{1}{n_{\mathrm{e}}}\left(\frac{2 \pi m_{\mathrm{e}} k T}{h^{2}}\right)^{\frac{3}{2}} \frac{2 U_{\mathrm{II}}}{U_{\mathrm{I}}} \mathrm{e}^{-\frac{E_{\mathrm{ion}}}{k T}}$$, suppose here $$n_e$$ is a constant.$$U_{II}$$ and $$U_{I}$$ are the partition function for Fe II and Fe I respectively, which are also constants. $$E_i$$ is the energy required to ionize one electron, which is obviously a constant. So as T increase, $$\frac{n_{II}}{n_{I}}$$ will increase. Because, it is relatively harder for ionize one more electron. So almost all of the Fe element are $$Fe I$$ or $$Fe II$$. Tues the strength of spectra line of $$FeI$$ will decrease as temperature increases. So star A is hotter.
2. As for $$H_{\gamma}$$, I have no idea about that. Although I can use Bolzmann equation to find relative number density of different state of hydrogen. But there are serval states. n=3 ,n=4, n=5.
• Exam question? What are your thoughts on the subject? May 7 at 6:30
• Have you heard of Doppler broadening? May 7 at 8:51
• astronomy.stackexchange.com/questions/27273/… May 7 at 10:38
• Welcome to astronomy SE! This question has the potential to be interesting, but without sources (of the graph), or additional background info this question has the potential to be downvoted. For more, please refer to How to Ask May 7 at 11:54
• See the question I've linked to which explains how Balmer lines change in strength with temperature. May 7 at 17:02