Should I provide a citation for atomic masses?
You can’t cite ‘a’ or ‘the periodic table’ because neither are published books. What you can do is state that you took the atomic masses as given by &lt;book&gt; or &lt;source&gt;.

I personally would not do that and I have not yet seen a research article that includes citations for what is considered a well-determined atomic property such as atomic mass or even electronegativity — even though the values for the latter vary greatly depending on source and method used. (Papers that discuss the difference between different definitions being the obvious exception.) Whether you are required to do that depends on what your TA or professor thinks. So go and ask them.