Atomic line spectra

Electrons in atoms can only exist in discrete energy levels. If an electron gains enough energy it can move up in energy level (this is known as excitation), however it will quickly return to its original energy level and release the energy it gained in the form of a photon of light.

Inside a fluorescent tube, electrons are accelerated, causing gas atoms to become excited and then de-excite, releasing photons. By passing the light from a fluorescent tube through a diffraction grating or prism, you get a line spectrum. Each line in the spectrum represents a different wavelength of light emitted by the tube. As this spectrum is not continuous but rather contains only discrete values of wavelength, the photon energies emitted will correspond to these wavelengths. This is evidence to show that the electrons in atoms can only transition between discrete energy levels

The difference between two energy levels is equal to a specific photon energy emitted by a fluorescent tube, or absorbed in a line absorption spectrum.

Therefore, you can calculate the energy of an emitted photon by using the following formula:

ΔE = E₁ − E₂ 

Where ΔE is the photon energy and E₁ /E₂ , represent energy levels.

Using the photon energy equation (E = hf), you can see that you can find the photon frequency by using the following equation:

Where f is the photon frequency and h is the Planck constant.