The Absorption & Emission of EM Radiation

EM Radiation and Atoms

Electromagnetic (EM) radiation is a form of energy that travels as waves and includes visible light, radio waves, X-rays, and more. Atoms can absorb and emit EM radiation, but only at specific wavelengths or frequencies. This happens because electrons in atoms exist in fixed energy levels or shells. When an electron moves between these energy levels, it must absorb or emit a photon of EM radiation with energy exactly equal to the difference between those levels.

The energy of a photon is related to its frequency by the equation:

$$E = hf$$

where:

• $E$ is the energy of the photon (in joules, J)
• $h$ is Planck6s constant (\(6.63 \times 10^{-34} \text{ Js}\))
• $f$ is the frequency of the EM radiation (in hertz, Hz)

Because each element has unique energy levels, the frequencies of EM radiation absorbed or emitted are unique to that element.

For instance, when an electron in a hydrogen atom moves from a lower to a higher energy level, it absorbs a photon with energy equal to the gap between those levels. Conversely, when it falls back down, it emits a photon with the same energy.

For example, if an electron moves from an energy level of $3.4 \times 10^{-19}$ J to $5.5 \times 10^{-19}$ J, the energy difference is:

$$5.5 \times 10^{-19} - 3.4 \times 10^{-19} = 2.1 \times 10^{-19} \text{ J}$$

This energy corresponds to the photon absorbed or emitted.

Absorption of EM Radiation

When atoms absorb EM radiation, electrons gain energy and move to higher energy levels, called excited states. This absorption only occurs if the energy of the incoming photon exactly matches the energy gap between the electron6s current level and a higher one.

The excited state is unstable, so electrons do not stay there long before returning to lower levels.

For example, if an electron in an atom is in the ground state (lowest energy level) and absorbs a photon with energy matching the gap to the next level, it will jump up to that level.

Emission of EM Radiation

After excitation, electrons return to lower energy levels, releasing energy as photons. The energy of the emitted photon equals the difference between the two energy levels.

This emission produces line spectra1 distinct lines at specific frequencies unique to each element. These lines correspond to the photons emitted when electrons drop between energy levels.

For example, if an electron falls from an energy level at $-3.0 \times 10^{-19}$ J to $-6.0 \times 10^{-19}$ J, the energy released is:

$$-3.0 \times 10^{-19} - (-6.0 \times 10^{-19}) = 3.0 \times 10^{-19} \text{ J}$$

A photon with this energy is emitted.

Line Spectra and Atomic Structure

Each element6s unique set of energy levels produces a unique line spectrum. This means the pattern of lines seen when atoms emit or absorb light acts like a fingerprint for that element.

This evidence supports Bohr6s atomic model, which proposed that electrons orbit the nucleus at fixed energy levels and that light is emitted or absorbed when electrons jump between these levels.

Spectral lines correspond directly to these electron transitions. By studying line spectra, scientists can identify elements in stars or gases without needing to physically sample them.

For example, hydrogen6s line spectrum has distinct lines in the visible range called the Balmer series, each corresponding to an electron falling to the second energy level from a higher one.