Absorption Spectra

When light containing many wavelengths passes through a cool, low-density gas, atoms in the gas can absorb certain wavelengths of that light.

The atoms do not absorb every wavelength. They absorb photons only when the photon energy matches an allowed energy difference between electron energy levels.

The missing wavelengths appear as dark lines in an otherwise continuous spectrum.

This pattern is called an absorption spectrum.

Absorption spectra provide powerful evidence for quantized energy levels and allow scientists to determine the chemical composition of objects that may be millions or even billions of light-years away.

How an Absorption Spectrum Forms

Imagine white light travelling through a cloud of cooler gas.

White light contains a broad range of wavelengths.

As the light passes through the gas:

1. photons interact with atoms
2. some photons have exactly the right energies to excite electrons
3. those photons are absorbed
4. electrons move to higher allowed energy levels
5. those wavelengths are removed from the light travelling directly toward the observer

When the remaining light is separated by wavelength, we see a continuous spectrum crossed by dark absorption lines.

The basic process is:

Continuous light → cooler gas → selected wavelengths absorbed → dark spectral lines

Electron Transitions During Absorption

Electrons in atoms can occupy only certain allowed energy levels.

Suppose an electron begins at:

E₁

and there is a higher allowed state:

E₂

For the electron to move from E₁ to E₂, it must gain exactly the required energy:

ΔE = E₂ − E₁

A photon can provide this energy.

If:

E_photon = ΔE

the photon can be absorbed and the electron can move to the higher level.

This is called an upward electron transition.

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Photons and Energy

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

E = hf

where:

E = photon energy

h = Planck's constant

f = frequency

Frequency and wavelength are related by:

c = fλ

Therefore, each allowed energy transition corresponds to a particular:

• photon energy
• frequency
• wavelength

Only photons with suitable energies can produce particular transitions.

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Why Doesn't the Atom Absorb Every Wavelength?

Suppose an electron requires:

3.0 eV

to move to the next allowed energy level.

A photon with energy:

3.0 eV

can cause that transition.

But a photon with:

2.5 eV

cannot simply move the electron partway between the two energy levels.

There is no allowed electron state there.

Similarly, in the simplified atomic model, a 2.9 eV photon cannot cause a transition requiring exactly 3.0 eV.

This is because atomic energy levels are quantized.

What Happens to the Absorbed Photon?

When an atom absorbs a photon, the photon's energy is transferred to the atom.

An electron moves to a higher-energy state.

The original photon is therefore no longer travelling along its original path toward the observer.

The excited electron may later return to a lower energy level and emit another photon.

However, that photon may be emitted in a different direction.

As a result, the original wavelength has reduced intensity along the observer's line of sight.

This produces a dark absorption line.

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Dark Does Not Mean No Light

An absorption line is often described as a dark line, but this does not necessarily mean absolutely zero light exists at that wavelength.

It means that the intensity at that wavelength is lower than the surrounding continuous spectrum.

Modern instruments measure these changes in intensity very precisely.

A spectrum plotted as intensity against wavelength may therefore show absorption lines as dips.

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Continuous Spectra

A hot, dense source can produce a broad, approximately continuous spectrum.

Examples include:

• stars
• hot solids
• dense glowing gases
• incandescent materials

If this light reaches us directly, we may observe a continuous range of wavelengths.

If it passes through cooler gas first, certain wavelengths can be absorbed.

The result is an absorption spectrum.

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Three Important Types of Spectra

It is useful to distinguish three basic types.

Continuous Spectrum

A broad, uninterrupted range of wavelengths.

Emission Spectrum

Bright lines at particular wavelengths against a darker background.

Absorption Spectrum

Dark lines at particular wavelengths within a continuous spectrum.

Emission vs Absorption Spectra

Emission and absorption spectra are closely related.

The important connection is that both are determined by the same atomic energy levels.

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The Same Energy Gaps

Suppose an atom can absorb a photon to move an electron:

E₁ → E₂

The required photon energy is:

ΔE = E₂ − E₁

Later, an electron making the reverse transition:

E₂ → E₁

can emit a photon with the same energy difference.

Therefore, an element's absorption and emission lines occur at characteristic corresponding wavelengths.

A Useful Analogy

Think of atomic energy levels as the floors of a building.

An electron cannot stop between floors.

To move from the first floor to the third floor, it must receive exactly enough energy for that transition.

During absorption:

photon energy → electron moves upward

During emission:

electron moves downward → photon energy released

The analogy is useful, but remember that atomic energy levels are not literal physical floors or distances.

They represent allowed energies.

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The Hydrogen Absorption Spectrum

Hydrogen has a characteristic set of allowed electron energy levels.

When continuous light passes through hydrogen gas, hydrogen atoms can absorb photons with energies corresponding to allowed upward transitions.

For visible wavelengths, important transitions include those beginning at:

n = 2

and moving to higher energy levels.

For example:

n = 2 → n = 3

n = 2 → n = 4

n = 2 → n = 5

n = 2 → n = 6

These correspond to the same characteristic wavelengths associated with visible Balmer emission lines, but the electron transitions occur in the opposite direction.

Hydrogen's Visible Absorption Lines

Important Balmer wavelengths include approximately:

In an absorption spectrum, these appear as reductions in intensity at those wavelengths.

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Comparing Hydrogen Emission and Absorption

Consider the hydrogen transition associated with approximately:

656 nm

During absorption:

n = 2 → n = 3

The electron absorbs a photon.

During emission:

n = 3 → n = 2

The electron emits a photon.

The direction of the electron transition is reversed, but the energy difference between the two states is the same.

Therefore, the characteristic wavelength is also the same.

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Why Every Element Has a Unique Absorption Spectrum

Different elements have different:

• nuclear charges
• numbers of electrons
• electron arrangements
• interactions between particles
• allowed atomic energy states

Therefore, different elements have different energy gaps.

Different energy gaps correspond to different photon energies.

Different photon energies correspond to different wavelengths.

Therefore:

each element produces a characteristic pattern of absorption lines.

This makes absorption spectra useful as atomic fingerprints.

Identifying an Element from an Absorption Spectrum

Suppose an unknown spectrum contains dark lines at:

410 nm

434 nm

486 nm

656 nm

These wavelengths closely match visible hydrogen Balmer wavelengths.

This provides evidence that hydrogen is present in the absorbing gas.

Scientists usually look for several matching lines, rather than relying on a single line.

Multiple matches provide much stronger evidence.

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Interpreting a Simple Absorption Spectrum

When examining an absorption spectrum:

Look for Dark Lines

Each dark line represents a wavelength where the intensity has been reduced.

Determine the Wavelengths

Use the wavelength scale to determine where the lines occur.

Compare with Reference Spectra

Look for matching patterns from known elements.

Look for Several Matches

One matching line may occur by coincidence.

Several matching lines provide stronger evidence.

Consider Multiple Elements

A real sample can contain many elements, so the observed spectrum may contain several overlapping patterns.

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Example: Identifying Two Elements

Suppose reference data show:

Element A: 410, 434, 486, 656 nm

Element B: 422, 527, 616 nm

An unknown spectrum contains absorption lines at:

410, 422, 434, 486, 527, 616 and 656 nm

The spectrum contains all four lines from Element A and all three from Element B.

Therefore, the evidence suggests that:

both Element A and Element B are present.

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Absorption Spectra and the Sun

One of the most famous examples of an absorption spectrum is the spectrum of the Sun.

The Sun's hot, dense interior produces a broad range of wavelengths.

This radiation passes through cooler gases in the Sun's outer layers.

Atoms in these cooler layers absorb particular wavelengths.

When sunlight is separated into a spectrum, numerous dark lines are visible.

These are called Fraunhofer lines.

Fraunhofer Lines

In the early nineteenth century, Joseph von Fraunhofer carefully studied the dark lines in the solar spectrum.

Thousands of absorption features can now be measured in sunlight.

These lines contain information about substances in the Sun's atmosphere.

By comparing solar absorption lines with laboratory spectra, scientists can identify elements present in the Sun.

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What Is the Sun Made Of?

Spectroscopy shows that the Sun contains large amounts of:

• hydrogen
• helium

and smaller quantities of many heavier elements.

Spectral features associated with elements such as:

• sodium
• calcium
• iron

can also be detected.

This is remarkable because scientists do not need to collect physical samples from the Sun.

They can analyse its light.

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Absorption Spectra in Astronomy

Astronomy depends heavily on spectroscopy because most astronomical objects are far beyond our physical reach.

Astronomers analyse light from:

• stars
• planets
• stellar atmospheres
• galaxies
• gas clouds
• some exoplanet atmospheres

The positions and patterns of absorption lines can reveal chemical composition.

Reading the Chemical Fingerprint of a Star

Imagine that a star's spectrum contains dark lines at the same wavelengths as laboratory hydrogen absorption lines.

That provides evidence that hydrogen is present in material interacting with the star's light.

Suppose additional lines match sodium and calcium.

Scientists can infer that these elements are also present.

The overall process is:

Observe star

↓

Separate its light into wavelengths

↓

Measure absorption lines

↓

Compare lines with laboratory spectra

↓

Identify elements

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Why Laboratory Spectra Are Important

Scientists can produce spectra of known substances in laboratories.

These become reference patterns.

When an astronomical spectrum is collected, its lines can be compared with these references.

A strong match between multiple lines provides evidence that the same element is present in the astronomical object.

This allows laboratory atomic physics to be applied to objects at enormous distances.

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Spectra Can Tell Us More Than Composition

Absorption spectra can reveal much more than which elements are present.

Scientists can also obtain information about:

• temperature
• density
• pressure
• motion
• magnetic fields
• chemical abundances
• conditions in stellar atmospheres

The shapes, strengths, widths and positions of spectral lines can all contain information.

At an introductory level, however, the most important use is:

identifying elements from characteristic spectral lines.

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Absorption Spectra and Motion

Suppose scientists know the normal laboratory wavelength of a particular absorption line.

If the same line appears at a slightly different wavelength in a star's spectrum, the shift can provide information about the star's motion.

This is related to the Doppler effect.

If spectral lines are shifted toward longer wavelengths, this is called a:

redshift

If they are shifted toward shorter wavelengths, this is called a:

blueshift

The important point is that scientists first need to know which spectral lines they are examining.

The characteristic atomic pattern provides that reference.

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Exoplanet Atmospheres

Absorption spectroscopy can even help scientists investigate some planets orbiting other stars.

When an exoplanet passes in front of its star, a small amount of starlight may pass through the planet's atmosphere.

Atoms and molecules in that atmosphere can absorb particular wavelengths.

Scientists can compare the spectrum during the transit with the normal stellar spectrum.

This can provide evidence about substances in the planet's atmosphere.

Worked Example: Energy of an Absorbed Photon

Suppose an atom absorbs light with wavelength:

λ = 500 nm

Convert to metres:

500 nm = 5.00 × 10⁻⁷ m

Use:

c = fλ

Rearrange:

f = c/λ

Using:

c = 3.00 × 10⁸ m/s

f = (3.00 × 10⁸)/(5.00 × 10⁻⁷)

f = 6.00 × 10¹⁴ Hz

Now use:

E = hf

with:

h = 6.63 × 10⁻³⁴ J·s

E = (6.63 × 10⁻³⁴)(6.00 × 10¹⁴)

E ≈ 3.98 × 10⁻¹⁹ J

Therefore, the electron absorbs approximately:

3.98 × 10⁻¹⁹ J

of energy.

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Worked Example: Comparing Two Absorption Lines

Suppose an atom absorbs photons at:

400 nm

and:

650 nm

Which transition requires more energy?

The shorter wavelength corresponds to the higher frequency.

Higher frequency means higher photon energy.

Therefore:

400 nm corresponds to the larger energy transition.

So:

400 nm photon → larger ΔE

650 nm photon → smaller ΔE

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Intensity and Absorption Lines

A spectrum can also be displayed as a graph of:

intensity vs wavelength

Instead of seeing dark vertical lines, absorption features appear as downward dips.

The horizontal axis represents wavelength.

The vertical axis represents the intensity of detected light.

A deeper dip means that less light was detected at that wavelength.

However, interpreting the exact depth of spectral lines can involve several physical factors, so line depth should not automatically be treated as a simple direct measurement of the amount of an element without further analysis.

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A Simple Spectrum Interpretation Strategy

When given a spectrum in a question:

First: identify whether it is continuous, emission or absorption.

Second: locate the important spectral lines.

Third: read their wavelengths.

Fourth: compare them with reference spectra.

Fifth: look for patterns of several matching lines.

Sixth: identify the element or elements that best match.

If the question involves electron transitions, remember:

Absorption → electron moves upward

Emission → electron moves downward

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Common Mistakes

Saying Dark Lines Are Emitted

Dark absorption lines represent wavelengths that have been removed or reduced from the observed continuous spectrum.

Thinking the Electron Moves Down During Absorption

Absorption supplies energy.

The electron moves to a higher-energy state.

Thinking Any Photon Can Be Absorbed

The photon must correspond to an allowed transition.

Thinking Electrons Can Stop Between Energy Levels

Atomic bound energy states are quantized.

Confusing Absorption with Emission

Absorption: photon absorbed, electron moves upward.

Emission: photon emitted, electron moves downward.

Thinking Emission and Absorption Lines Occur at Completely Different Wavelengths

For the same element and corresponding transitions, characteristic wavelengths are related to the same energy gaps.

Thinking a Dark Line Means Absolutely No Light

It generally indicates reduced intensity at that wavelength.

Identifying an Element from One Line Alone

Several matching spectral lines provide stronger evidence.

Thinking Every Absorption Line Is Visible

Many important lines occur in ultraviolet or infrared regions.

Assuming Every Dark Line Belongs to One Element

Real spectra can contain absorption features from many different atoms, ions and molecules.

Assuming Line Depth Alone Gives the Amount of an Element

Spectral line strength can depend on several physical conditions.

Forgetting to Convert Nanometres to Metres

For calculations:

1 nm = 1 × 10⁻⁹ m

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Key Terms

Absorption spectrum — A spectrum containing reduced intensity at particular wavelengths because radiation has been absorbed.

Absorption line — A dark line or intensity dip corresponding to a wavelength that has been absorbed.

Continuous spectrum — A broad, uninterrupted range of wavelengths.

Emission spectrum — A spectrum containing radiation emitted at particular wavelengths.

Line spectrum — A spectrum containing distinct spectral features at particular wavelengths.

Photon — A discrete packet of electromagnetic energy.

Absorption — The transfer of photon energy to matter.

Electron transition — A change of an electron from one allowed energy state to another.

Upward transition — A transition to a higher-energy state caused by energy absorption.

Downward transition — A transition to a lower-energy state, often accompanied by photon emission.

Ground state — The lowest allowed atomic energy state.

Excited state — An allowed state with energy greater than the ground state.

Quantized energy — Energy restricted to particular discrete allowed values.

Energy gap — The difference in energy between two allowed states.

Wavelength — The distance between equivalent points on successive waves.

Frequency — The number of wave cycles passing a point each second.

Intensity — A measure related to the amount of radiation detected.

Spectral line — A feature appearing at a particular wavelength in a spectrum.

Atomic fingerprint — The characteristic pattern of spectral lines associated with an element.

Spectroscope — An instrument used to separate light according to wavelength.

Spectrometer — An instrument used to measure a spectrum quantitatively.

Spectroscopy — The study and measurement of interactions between electromagnetic radiation and matter.

Fraunhofer lines — Absorption features observed in the solar spectrum.

Balmer series — Hydrogen spectral lines associated with transitions involving n = 2.

Redshift — A displacement of spectral features toward longer wavelengths.

Blueshift — A displacement of spectral features toward shorter wavelengths.

Transmission spectroscopy — Analysis of wavelengths transmitted through a material, such as an atmosphere, to determine what has been absorbed.

Reference spectrum — A known spectrum used for comparison with an unknown spectrum.

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Key Takeaways

• An absorption spectrum forms when radiation passes through matter that absorbs particular wavelengths.
• A common astronomical absorption spectrum occurs when continuous radiation passes through cooler gas.
• Absorbed photons transfer energy to atoms.
• During absorption, electrons move from lower to higher allowed energy states.
• The photon must have an appropriate energy for the transition.
• Atomic energy levels are quantized.
• Electrons cannot simply occupy arbitrary energies between allowed bound states.
• Photon energy is related to frequency by:

E = hf

• Frequency and wavelength are related by:

c = fλ

• Shorter wavelengths correspond to higher photon energies.
• An absorption spectrum usually appears as dark lines within a continuous spectrum.
• The dark lines represent wavelengths with reduced intensity.
• Emission involves downward electron transitions.
• Absorption involves upward electron transitions.
• Emission and absorption features of the same element are related to the same atomic energy differences.
• Different elements have different energy-level structures.
• Each element therefore produces a characteristic pattern of spectral lines.
• These patterns can act as atomic fingerprints.
• Several matching lines provide stronger identification than one line.
• Hydrogen produces characteristic absorption lines associated with its allowed energy transitions.
• The Sun's spectrum contains many absorption features known as Fraunhofer lines.
• Astronomers compare stellar spectra with laboratory reference spectra to identify elements.
• Absorption spectroscopy allows scientists to study objects without physically collecting samples.
• Spectra can provide information about composition and, with further analysis, temperature, motion and other physical conditions.
• Absorption spectroscopy can also help investigate some exoplanet atmospheres.

The central idea is:

Specific atomic energy levels → specific energy gaps → specific photons absorbed → specific dark spectral lines

And the simplest comparison is:

Absorption: photon in → electron up

Emission: electron down → photon out