A mixture of hydrogen and neon is heated until it is luminous. Describe what is seen when this light passes through a prism and is projected onto a screen.

Dispersion of light is a captivating phenomenon that we can observe in our daily lives, just think of a rainbow. When light encounters a material such as a prism, its components of various wavelengths bend at different angles. This happens because different colors of light travel at different speeds when they pass through a medium other than vacuum.

White light, which comprises a spectrum of colors, separates into a beautiful array of its constituent colors—red, orange, yellow, green, blue, indigo, and violet. This occurs because each color has a different wavelength; red light has the longest wavelength and violet has the shortest. When passing through a prism, violet light bends the most while red bends the least due to their respective speeds in the medium.

In the context of the exercise, the gaseous mixture of hydrogen and neon, when heated, emits light. This light, when passed through a prism, disperses into its component wavelengths, revealing the distinct spectral lines corresponding to each gas.

The Balmer series is essential in understanding the unique spectral fingerprint of hydrogen. Named after Johann Balmer, who discovered this series in 1885, it consists of all the electromagnetic transitions of electrons in a hydrogen atom from higher-energy levels to the n=2 orbit.

What makes the Balmer series fascinating is that it lies in the visible region of the electromagnetic spectrum, which means we can actually see these lines as different colors. They include four notable lines which are often referred to by their alphabetical designation: H-alpha (red), H-beta (blue-green), H-gamma (blue), and H-delta (violet).

Each line in the Balmer series corresponds to an electron falling from a higher energy level to the second energy level. For example, H-alpha results from a transition from the n=3 to the n=2 level. In the exercise, when the emitted light from hydrogen is passed through a prism, the individual lines of the Balmer series can be distinguished on the projected screen.

Diving deep into the atomic scale, atomic energy levels represent the regions around the nucleus where electrons reside. These levels are quantized, meaning that electrons can only occupy certain regions of space, or orbitals, with specific energy amounts.

Electrons can move between these levels by either absorbing or emitting energy in quantized packets known as photons. When an electron jumps to a higher energy level – a process known as excitation - it absorbs a photon. Subsequently, when it falls back down to a lower level, it emits a photon of light. The energy of this emitted photon corresponds to the energy difference between the two levels.

Each element has a unique set of energy levels and therefore emits or absorbs photons of only certain energies. This results in a unique spectral signature for each element, which is used extensively in techniques such as spectroscopy to identify the chemical composition of stars and other celestial objects. In the textbook exercise, both hydrogen and neon display their atomic fingerprints on the screen, and these spectral lines depicted are direct consequences of the discrete atomic energy levels within their atoms.