Properties of Photons
Convert wavelength to frequency and photon energy; distinguish photon energy from light intensity.
AP Chemistry Topic 3.12 · CED printed p. 71 / PDF p. 78. This teaching, practice and feedback were added for the AP edition; original author material remains separately traceable.
Before you start
- Scientific notation and unit conversion
- Electronic transitions
One photon has a definite energy
For electromagnetic radiation in vacuum, , with wavelength λ in meters, frequency ν in s−1 and c the speed of light. Photon energy is . Shorter wavelength means higher frequency and higher energy per photon. In transparent media, wavelength and speed can change, while frequency is maintained across a boundary; use the supplied vacuum relationship in these AP calculations.
Use c ≈ 3.00 × 108 m s−1 and h ≈ 6.626 × 10−34 J s unless the task supplies other rounding. The SI values are exact as definitions, but measured wavelength still limits result precision. Convert nm to m with 1 nm = 10−9 m. E comes out as joules per photon, not automatically joules per mole. Multiply by NA only when a mole of photons is requested.
The species and photon exchange the same gap energy
An absorbed photon increases the species’ energy by the photon’s energy. An emitted photon decreases it by the same amount. For an allowed discrete transition, . The photon’s energy is positive; the sign of the species’ change depends on absorption (+) or emission (−). A larger emission gap gives a shorter wavelength.
Brightness and photon energy are different. At fixed frequency, making light more intense generally means more photons arriving per unit time, not a larger energy per photon. A photon with unmatched energy does not automatically create a particular discrete transition; molecular bands and other processes need the relevant allowed states. State that model when reading an energy-level diagram.
Let's work through it
Work it through
An allowed transition absorbs 500. nm light. Use h = 6.626 × 10−34 J s, c = 3.00 × 108 m s−1, and NA = 6.022 × 1023 mol−1.
- Convert λ = 500. × 10−9 m = 5.00 × 10−7 m.
- Frequency ν = c/λ = 6.00 × 1014 s−1.
- E = hν = 3.9756 × 10−19 J per photon → 3.98 × 10−19 J. The absorbing species gains that energy.
- For a mole of such photons, multiply by NA: 239 kJ mol−1. For the reverse emission, the species’ energy change is negative while emitted photon energy remains positive.
Try it from memory
Pause & retrieve
Try it before you peek.
Write your answer and the reason from memory. Then compare with the worked answer. Your self-assessment is a study decision, not an automatically graded score.
Question 1
If wavelength doubles in vacuum, what happens to frequency and photon energy?
See every recall question with its answer
These references preserve each prompt and its answer for direct evidence links. Try the interactive questions above before opening the worked reasoning.
Retrieval 1
If wavelength doubles in vacuum, what happens to frequency and photon energy?
Worked answer and reason
Both halve.
c is fixed and E is proportional to frequency.
Retrieval 2
What sign is the species’ energy change in emission?
Worked answer and reason
Negative; the positive-energy photon carries away that energy.
The sign describes the species, not a negative-energy photon.
Retrieval 3
Does brighter monochromatic light necessarily have more energetic photons?
Worked answer and reason
No. At the same frequency, each photon’s energy stays hν; increased intensity usually changes photon arrival rate.
Photon energy depends on frequency, not intensity alone.
Catch the tempting mistake
- 500 nm can be inserted as 500 m in hc/λ.
- Convert to meters; the mistake changes energy by a factor of a billion.
- An emitted photon has negative energy.
- The species loses energy; the photon carries positive energy away.
- E = hν always gives energy per mole.
- It gives per photon; multiply by Avogadro’s constant for molar energy.
Put it to work
Give the chemical reason as well as the calculation. Worked solutions are on a separate page.
- Unit 3 problem 28 · ap application · symbolic
- Unit 3 problem 29 · ap synthesis · data
- Unit 3 problem 30 · ap application · multiple
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For the teacher
- Require the wavelength unit conversion before substitution.
- Ask students to state species ΔE sign and photon E sign separately.
Source objectives and scope
Source edition: ap-chemistry-ced-fall2024-local-b5dfe867. See this topic in the course outline →
- 3.12.A
- Explain the properties of an absorbed or emitted photon in relationship to an electronic transition in an atom or molecule.
- 3.12.A.1
- When a photon is absorbed (or emitted) by an atom or molecule, the energy of the species is increased (or decreased) by an amount equal to the energy of the photon.
- 3.12.A.2
- The wavelength of the electromagnetic wave is related to its frequency and the speed of light by the equation: EQN: c = λν. The energy of a photon is related to the frequency of the electromagnetic wave through Planck’s equation: EQN: E = ℎν.
Science references for this teaching
- AP Chemistry Course and Exam Description, effective Fall 2024 (supplied source) — Exact topic-numbered learning objectives, essential knowledge, science practices and AP exclusions; supplied PDF SHA256 b5dfe8677ef3d88c613865d2e2a3e8d6125d652e2b24c71ef1e8ce4e011094f0.
- OpenStax Chemistry 2e §6.1, Electromagnetic Energy — Wavelength-frequency-energy relationships and photon energy units.
- NIST 2022 CODATA complete constants table — Exact SI Avogadro, Planck and light-speed constants; rounded values supplied explicitly in assessment tasks.
Glossary and deeper reading · 3 refreshers
These editorial refreshers supplement the reading. Definitions and examples are added guidance; original source wording and recorded answers remain in their original context.
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Absorbance
Absorbance is a logarithmic measure of how much a sample reduces transmitted light at a specified wavelength. It depends on the ratio of incident to transmitted intensity rather than simply being the fraction absorbed. For example, absorbance 1 corresponds to transmission of one-tenth of the incident intensity.
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Photon
A photon is a quantum of electromagnetic radiation. Its energy increases with frequency and decreases as wavelength increases. For example, a blue-light photon carries more energy than a red-light photon.
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Mole
A mole is an amount of substance containing exactly 6.02214076 × 10²³ specified entities. The entities can be atoms, molecules, ions, or formula units, so the counted entity must be named. For example, one mole of oxygen molecules contains two moles of oxygen atoms.