The instruments to do The testing you want are complicated. It's not that the spectrometer couldn't be used, but it would take a lot of work. Here is a little background.
The common way to do this is with analytical techniques, such as atomic absorption (AA), atomic emission (AE), or inductively coupled plasma ( ICP).
All use a spectrometer or spectrophotometer, so it is possible. It's the extras the instruments have that make it hard.
The ICP takes high power and a plasma furnaces. It's not easy to do. They were in the $100k range (base). That's the first one to eliminate.
The AA takes special lamps for each element analyzed. Sometimes you can combine multiple elements into one lamp, but not always. AE doesnt take the lamp, but it is often the less sensitive of the two.
With all three techniques, the metal must be prepped. This usually means just acid digestion, although it can be much more involved. All forms of the metal ( say chrome) must be in the same valence state. Sometimes, a fair number of chemical steps are required. Then the dissolved liquids are aspirated in a flame and the spectra is taken.
Many of the lines used in these techniques are in the UV. i.E. Zinc is usually analyzed at 213.9 nm. There are many interferences from flames, etc, that need to be worked through.
Good luck with your project.