Absorption and Excitation

Introduction

An atom in a lower energy state can absorb light and move to a higher allowed state. The absorbed photon's energy must match the difference between those states for that particular bound–bound transition. This explains why an atomic gas can remove specific wavelengths from broad light. Excitation raises an atom's energy; it does not necessarily remove an electron.

Core explanation

In an energy-level diagram, place lower atomic states toward the bottom and higher states above. A photon of energy E photon = hν can be absorbed if it supplies an allowed energy difference E high − E low. The atom's energy increases by that positive amount. For hydrogen in Bohr's model, an electron at n = 1 can reach n = 2 by absorbing a photon whose energy matches E₂ − E₁, about 1.64 × 10⁻¹⁸ J with rounded level values. The electron remains bound at n = 2; the atom is excited, not ionised.

If a photon has the wrong energy for an available discrete bound-state transition, it is not simply absorbed into a halfway state. The allowed-level model does not include arbitrary positions between levels. In a real sample there can be other interactions, broadened lines, molecules or ionisation processes, so “not absorbed” must be tied to the particular isolated-atom transition being considered. The simple rule is exact matching for a named bound–bound jump within the idealised model.

Ionisation is different. Removing the electron from a bound atom requires enough energy to reach the unbound continuum. In hydrogen, the ground-state ionisation energy is about 2.18 × 10⁻¹⁸ J per atom. A photon with more than that threshold can ionise ground-state hydrogen; excess energy can become kinetic energy of the released electron. Thus one should not say every absorption requires exact equality to one discrete bound-level gap. Exact matching is the appropriate rule for a specific bound-state excitation, while continuum absorption has a threshold.

Absorption lines can be observed when broad light travels through a cooler gas. Atoms remove photons at wavelengths that match available transitions from populated lower states, leaving dips in the transmitted spectrum. The gas may later re-emit light in other directions, so “absorbed” does not mean energy has vanished forever. The observed dark line depends on the source–gas–detector geometry and on whether relevant atoms occupy the starting state.

Population matters. Most hydrogen atoms at ordinary low excitation are in or near the ground state, so upward transitions from n = 1 may be more available than transitions from rare highly excited starting states. A line requiring an atom initially at n = 2 will be weak if almost no atoms occupy n = 2. This is why simply listing all mathematical level differences does not guarantee every line is visible in every experiment.

The word “electron absorbs a photon” is a convenient shorthand. The atom as a quantum system changes state, and the photon ceases to exist as a separate photon in the ideal absorption event. Drawing an electron climbing a ladder is a model for the energy change, not a filmed trajectory through the space between levels. Modern quantum theory explains transitions without a tiny particle walking along an arrow.

Absorption connects to chemical applications. Atoms and molecules can absorb selected light, allowing spectrometers to infer composition or concentration when calibrated. Molecular spectra add vibrational and rotational features, so the simple hydrogen diagram is a starting example rather than a universal spectral catalogue.

Step-by-step reasoning

1. Identify the atom's initial allowed energy state and the proposed higher state. 2. Compute or read ΔE = E high − E low, a positive value. 3. Compare photon energy hν or hc/λ with ΔE for that bound-state transition. 4. State excitation if the electron remains bound, or ionisation if enough energy removes it.

Visual explanation

Draw horizontal n = 1 and n = 2 lines. Place an upward arrow labelled “one matching photon absorbed” and write ΔE = E₂ − E₁ beside it. Draw a separate arrow past a zero-energy threshold labelled “ionisation,” making the distinction visual.

Real-world analogy

A machine with fixed settings may move from one setting to another only when the right amount of input is supplied. The analogy helps with discrete bound levels. Real atoms are quantum systems, however, and sufficiently energetic light can remove an electron rather than selecting a higher bound setting.

Real-world example

Light from a broad source passing through a cool atomic gas can emerge with particular wavelengths weakened. Those absorption lines reveal energies the gas atoms can take up from populated lower states and can help identify the species when several lines are compared.

Why?

Why does an atom not settle halfway between two allowed states after absorbing a smaller photon? In the bound-state model, that intermediate energy is not an allowed stationary state. For the named transition, the photon energy must match the full gap.

Common misconception

“Any photon with more energy than an excitation gap automatically produces that same bound excited state.” Bound–bound absorption requires the matching gap in the ideal model. A much higher-energy photon may instead ionise or interact by another permitted process.

Worked example

Hydrogen has E₁ = −2.18 × 10⁻¹⁸ J and E₂ = −5.45 × 10⁻¹⁹ J in a rounded Bohr model. To excite from n = 1 to n = 2, calculate E₂ − E₁ = 1.635 × 10⁻¹⁸ J. A photon with that energy can supply the transition. The atom's energy increases; the photon is absorbed. The electron remains bound because E₂ is still below the zero-energy limit.

Quick check

1. Does a hydrogen electron at n = 2 remain bound or become ionised? Answer: It remains bound in an excited allowed state; ionisation reaches the unbound continuum.

Exam focus

Use final minus initial atomic energy for absorption and express the result as positive photon energy. State the starting level, because not every atom can absorb through every mathematical level gap at a given moment. Distinguish bound excitation from ionisation.

Advanced insight

Quantum transition probabilities and selection rules determine which mathematically possible energy differences produce strong spectral lines. Line widths arise from finite lifetimes, motion and interactions. “Exact matching” is the ideal-level statement; real spectra have finite bandwidths and more than one interaction channel.

Summary

Absorption raises an atom from one allowed bound state to another when a photon matches the gap. The resulting state is excited but still bound. A sufficiently energetic photon can instead ionise an atom, and observed absorption lines also depend on state populations and experimental geometry.

Practice questions

1. Write the energy equation for an upward bound-state transition. Answer: E photon = E high − E low = hν. 2. Is an atom at n = 3 necessarily ionised? Answer: No. A finite Bohr n level is bound; ionisation reaches the unbound limit. 3. Why can a gas remove selected wavelengths from broad light? Answer: Its atoms absorb photons matching allowed transitions from populated lower states. 4. What happens to excess photon energy in photoionisation above threshold? Answer: It can appear as kinetic energy of the released electron, rather than a halfway bound state.