Hydrogen Line - Cause

Cause

• Origin of neutral hydrogen emission

• An electron orbiting a proton with parallel spins (pictured) has higher energy than if the spins were anti-parallel.

• Fine and hyperfine structure in hydrogen. The hyperfine splitting of the ground 2S state is the source of the 21 cm hydrogen line.

• Electron transitions and their resulting wavelengths for hydrogen. Energy levels are not to scale.

Neutral hydrogen consists of a single proton orbited by a single electron. As well as their orbital motion, the proton and electron also have spin. Classically, this is analogous to rotational motion (like the Earth rotating on its axis as it orbits the Sun), but as they are quantum particles the concept has a slightly different meaning.

The spin of the electron and proton can be in either direction - in the classical analogy they are rotating clockwise or anticlockwise around a given axis. They may have their spin oriented in the same direction or in opposite directions. Because of magnetic interactions between the particles, a hydrogen atom that has the spins of the electron and proton aligned in the same direction (parallel) has slightly more energy than one where the spins of the electron and proton are in opposite directions (anti-parallel). The fact that the lowest-energy configuration arises in the anti-parallel spin configuration is an inherently quantum-mechanical result. A proton and electron with anti-parallel spins have parallel magnetic moments owing to their opposite charge. Classical mechanics would predict that this configuration should have higher energy, but a more detailed quantum mechanical analysis shows that the opposite is true.

The lowest orbital energy state of atomic hydrogen has hyperfine splitting arising from the spins of the proton and electron changing from a parallel to antiparallel configuration. This transition is highly forbidden with an extremely small probability of 2.9×10−15 s−1.

This means that the time for a single isolated atom of neutral hydrogen to undergo this transition is around 10 million (107) years and so is unlikely to be seen in a laboratory on Earth. However, as the total number of atoms of neutral hydrogen in the interstellar medium is very large, this emission line is easily observed by radio telescopes. Also, the lifetime can be considerably shortened by collisions with other hydrogen atoms and interaction with the cosmic microwave background.

The line has an extremely small natural width because of its long lifetime, so most broadening is due to doppler shifts caused by the motion of the emitting regions relative to the observer.