we just did an experiment on spectral fingerprinting and i was just curious, what if the elemental vapors were mixed in one discharge tube, how can i know what the individual elements are?

You see all the spectral lines, and can see each element, just as when one examines the lines from the Sun: you see all elements.

how can i distinguish one element's spectral lines from the other?

To determine the individual elements when the elemental vapors are mixed in one discharge tube, you can use a technique called spectral analysis. Spectral fingerprinting, also known as spectroscopy, is the study of the interaction between matter and electromagnetic radiation.

Here's how you can analyze the mixed elements using spectroscopy:

1. Collect the mixed element discharge tube: Ensure that the discharge tube contains a mixture of elemental vapors you want to analyze. For example, if you have a mixture of hydrogen and helium, the discharge tube should contain both.

2. Set up the spectroscopy apparatus: Use a spectrometer or a spectrophotometer to observe the spectrum of light emitted by the mixed discharge tube. This apparatus will measure the wavelengths of light emitted by the elements.

3. Observe the emitted light: Energize the discharge tube to produce a plasma or gas excited state. As the electrons in the excited state return to their ground state, they release energy in the form of light. Each element emits light at specific, characteristic wavelengths, creating a unique spectral fingerprint.

4. Analyze the spectrum: Use the spectrometer or spectrophotometer to measure the wavelengths of light emitted by the mixed elements. Compare these measured wavelengths to known emission spectra of various elements. These known spectra can be obtained from reference databases or books on atomic physics.

5. Identify the elements: Match the measured wavelengths to the known emission spectra of individual elements. By comparing the observed spectral lines to the known spectral lines of different elements, you can identify which elements are present in the mixed discharge tube.

6. Cross-reference and verification: To ensure accuracy, cross-reference the results with known properties of the elements present in the mixture. Compare the measured wavelengths and intensities with established data to confirm the identification of each element.

It's important to note that spectroscopy is a widely used technique, and there are specialized instruments designed to analyze mixtures of elements. These instruments use more advanced algorithms and calibration techniques to identify multiple elements simultaneously.

By following these steps and using the principles of spectroscopy, you can determine the individual elements present in a mixture of elemental vapors in a discharge tube.