Line Spectra of Hydrogen — Definition

Definition

Imagine shining white light, which contains all colors, through a prism. It splits into a continuous rainbow, right? That's a continuous spectrum. Now, imagine exciting hydrogen gas, perhaps by passing an electric current through it.

When this excited hydrogen gas emits light, and you pass that light through a prism, you don't see a continuous rainbow. Instead, you see only a few distinct, bright lines of specific colors, separated by dark regions.

This is what we call an 'emission line spectrum'. Each line corresponds to a very precise wavelength of light.

Conversely, if you pass a continuous spectrum of white light through cool hydrogen gas, the gas will absorb specific wavelengths of light. When you then analyze the light that passes through, you'll see a continuous spectrum with dark lines at precisely the same wavelengths where the excited hydrogen gas emitted bright lines. This is an 'absorption line spectrum'.

Why does hydrogen behave this way? The classical physics of Newton and Maxwell couldn't explain it. It was Niels Bohr who, in 1913, proposed a revolutionary model for the hydrogen atom. Bohr suggested that electrons in an atom don't orbit the nucleus randomly but only in specific, stable orbits, each associated with a definite amount of energy.

These are called 'stationary states' or 'energy levels'. An electron in a particular orbit has a specific energy, and it doesn't radiate energy as long as it stays in that orbit.

When an electron jumps from a higher energy level to a lower energy level, it emits the difference in energy as a photon of light. The energy of this photon is directly related to its frequency and wavelength ($E = h\nu = hc/\lambda$).

Since the energy levels are discrete, the energy differences are also discrete, leading to the emission of light at only specific, discrete wavelengths – hence, a line spectrum. Similarly, for absorption, an electron absorbs a photon of exactly the right energy to jump from a lower to a higher energy level.

For hydrogen, these energy levels are denoted by principal quantum numbers, $n = 1, 2, 3, \dots$, where $n=1$ is the ground state (lowest energy). Transitions ending at $n=1$ form the Lyman series (ultraviolet), transitions ending at $n=2$ form the Balmer series (visible), $n=3$ the Paschen series (infrared), and so on.

The study of these line spectra was crucial in validating Bohr's model and laid the groundwork for modern quantum mechanics, providing a fundamental understanding of atomic structure and light-matter interaction.