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.
Thanks! I really appreciate this answer.
I would like to answer your question in a different way:
1. In order to analyse a metal (by atomic emission spectrometry, AE), you need to put your solid metal into atoms. This is easiest done by an electric spark or arc. (The spark plug is atomizing its électrodes. By observing these sparks, one could "analyse" the metal of the électrodes.)
2. Each chemical element emits at many wavelenths (lines), specially the element Fe (iron). In order to "separate" one line of e.g. Fe from a line of e.g. Cr, one needs a spectrometer with a good resolution, probably 100 times better than the homemade spectrometer. Also, some important elements (in steel) like C, P, S emit only good lines at short wavelengths, where the lines are absorbed by the air. One needs a "vacuumspectrumeter".
3. If one wants to know how much of an element is in the metal, one needs to "calibrate" the instrument. By measuring the intensity of the spectral line in several samples of known content, one can establish a "calibration curve" and the determine the concentration in the unknown sample.
But the short answer to your question is: NO!