The Relationship Between Emission Wavelength and Photon Energy in Metallic Ions

This investigation explores the relationship between emission wavelength and photon energy in metallic ions using flame test analysis. The research question is: How does the observed photon color and predicted metallic wavelength (nm) of different metallic ions impact the energy (J) emitted? The researchers hypothesized an inverse relationship between the variables: as the wavelength increases, the energy emitted will decrease.

To investigate these ideas, wooden splints were soaked in 1.0 M solutions of various metal chlorides and exposed to a flame emitted from a Bunsen burner. The flame colors emitted as a result of the contact between heat and the metallic solutions were qualitatively observed and utilized to estimate frequency and energy.

The processed data later revealed a clear inverse relationship between wavelength and energy, supported by a near-perfect linear correlation. Metals emitting a shorter wavelength (e.g., potassium) exhibited higher photon energies, while those with longer wavelengths (e.g., lithium) showed lower energies. Relatively low percent error values demonstrated reasonable accuracy, though limitations arose from subjective color estimation and inconsistent flame conditions.

In the end, the results support the hypothesis and align with established quantum theory, confirming that photon energy is inversely proportional to wavelength. Beyond this experiment, this relationship has important real-world applications in fields such as spectroscopy, astronomy, and modern technologies, including lasers, fireworks, and medical imaging.