Your Project Description section should answer three basic questions. You could use \subsection do separate these sections from each other, but you don't have to. It should be clear from your writing what question you are addressing. Each section should be about 2/3 of a page to one page long.
In the first section, you should give the reader context: what is the question you are trying to answer? What work has been done so far? What do the important terms mean? After finishing this section, the reader should have a clear sense of the basics she will need to know to understand the work you are doing. You should be writing to an audience who know basic physics, but are ignorant of the specifics of this particular question. Imagine your classmates as the ones reading what you are writing.
Remember that when you write this, you are synthesizing the material that you read. A good way to deal with citations is to summarize the issue generally in your own words, and then close the paragraph with an example from the literature that illustrates and makes it more specific. For example, you could describe the basic concept behind the photoelectric effect, and then close with "This would imply that light can be treated as many individual particles (Einstein, 1905)." Another way is to start off with the citation, like "Einstein (1905) proposed that light might be quantized into packets of energy. He said..." The important thing is that whenever you make a claim, you need to support it with evidence in the form of a citation that could, in principle, be checked by the reader.
We're playing a bit of a game here, in that you are proposing to do an old experiment as if it were new. This complicates the citation question. You should treat your experiment as if you are confirming someone else's controversial results. For example, you could say "Compton (1923) recently reported that x-ray recoil off electrons as if they were relativistic particles. We propose to verify his results by carrying out a similar experiment." Then you go on to explain the experiment you will do and how it is similar to and different from Compton's.
In this subsection, you address the "broader impact". In other words, why should anyone care about the value of the constant you want to measure? If it's important that we know the speed of light, explain why. You have a bit of an advantage here, because you can look at what people have actually done with the knowledge, and write that in the future tense (you should still cite their work, of course).