Atomic energy levels underpin the interpretation of stellar spectra and form the essential quantum basis for understanding how atoms absorb and emit electromagnetic radiation observed from astronomical sources.

Atomic energy levels describe the fixed energies an electron in an atom may possess, shaping how atoms interact with radiation and enabling scientists to decode stellar composition through spectral observations.

Energy Levels in Isolated Atoms

In astrophysics, understanding atomic energy levels is crucial because light from stars carries information about the physical conditions and elements present in stellar atmospheres. Electrons bound to an atom do not behave like classical particles and cannot adopt arbitrary energies; instead, they are restricted to a set of well-defined values.

These levels arise from the quantum mechanical nature of electrons, which are described by wavefunctions obeying the Schrödinger equation. Only certain standing-wave patterns are physically allowed, giving rise to quantisation. This forms the basis for why atomic spectra consist of narrow, characteristic lines.

Electrons closest to the nucleus occupy the most stable and lowest-energy positions. As electrons move further from the nucleus, their energy increases but remains constrained within allowed levels until they reach the ionisation limit, where they become free of the atom.

Negative Energy Levels and the Zero-Energy Continuum

A key feature stressed in the OCR specification is that all permitted energy levels for a bound electron are negative.

Energy levels of the hydrogen atom plotted with negative energies, converging toward the zero-energy continuum. The decreasing spacing at higher levels shows how states crowd near ionisation. Labels clearly distinguish the ground state and successive excited states. Source.

Because bound electrons exist in states with energies below this point, their energy values are expressed as negative numbers. The most negative value corresponds to the ground state, which is the lowest available energy configuration for the electron.

After discussing the continuum, it becomes helpful to consider how electrons gain or lose energy to move between levels.

Ground State and Excited States

Electrons naturally tend to occupy the lowest energy arrangement possible. This stable configuration is known as the ground state.

When energy is absorbed from radiation or collisions, an electron may move to a higher energy level.

A single sentence to separate definition blocks is required before introducing a new definition about excited states.

Excited states are inherently unstable, so electrons eventually return to lower levels. When they do, they release energy, typically in the form of electromagnetic radiation.

Diagram of photon absorption and emission between quantised levels. Upward arrows show excitation into higher states, while downward arrows mark emission as electrons return to lower levels. The minimal French labels correspond only to “excitation” and “dé-excitation” and do not add extraneous syllabus content. Source.

The differences between allowed energy values determine the wavelengths of emitted or absorbed photons. Although detailed relationships involving frequency and wavelength are introduced in later subsubtopics, it is important here to appreciate that only specific transitions are possible, producing the discrete spectra observed in astronomy.

Quantisation and Line Spectra

Quantisation is the reason why atoms produce line spectra rather than continuous spectra. Each line corresponds to a transition between two permitted energy levels, and because these differences vary uniquely for each element, the resulting pattern acts as a spectral fingerprint. However, the full use of spectral fingerprints belongs to a later subsubtopic; here the focus remains on how energy levels underpin the process.

Key features of quantised levels include:

• Fixed energy differences between levels, leading to discrete patterns in absorption and emission.

• Element-specific arrangements of levels determined by nuclear charge and electron configuration.

• Increasing level spacing near the continuum, where energies become less negative and transitions are more closely spaced.

These patterns are directly relevant in astrophysics, where telescopes equipped with spectrometers analyse the light from stars to infer their atmospheric composition and temperature.

Energy-Level Diagrams and Atomic Structure

Students often use energy-level diagrams to visualise the structure of quantised atomic states. These diagrams typically represent:

• Horizontal lines for each permitted level.

• The ground state as the lowest line.

• Increasingly higher, less negative levels approaching the continuum.

• The continuum itself shown as a boundary above which the electron is free.

Such diagrams assist in explaining why atoms interact with particular wavelengths of light. Only transitions between allowed levels are permitted, so the diagram acts as a map of possible photon absorptions and emissions.

Relevance to Astrophysics

Understanding atomic energy levels is essential when interpreting stellar radiation. Because atoms in stellar atmospheres absorb only specific wavelengths, astronomers can determine:

• Which elements are present in a star.

• Whether electrons in those atoms are largely in their ground states or excited states.

• How temperature affects the population of energy levels, influencing the appearance of the absorption lines.

This subsubtopic provides the foundational quantum framework required for later parts of the OCR specification dealing with spectral lines, transition energies, and the use of spectroscopy in astrophysical investigations.