AP Chemistry Photon Energy
Using E = hν and c = λν, converting to kJ/mol, and deciding what a photon can do, in four worked examples.
Photon questions combine three ideas: the equations that tie wavelength, frequency, and energy together; a conversion from one photon to one mole; and a comparison with a bond enthalpy or ionization energy. Each is simple on its own, and the exam tends to chain them. The Unit 3 review shows one photon calculation; this page adds the reverse direction, the mole conversion, and the link to bond breaking and electron removal.
The Photon Equations and the Spectrum Regions
- c = λν relates the speed of light (2.998 × 108 m/s) to wavelength and frequency.
- E = hν gives the energy of one photon, with h = 6.626 × 10−34 J·s.
- E = hc/λ combines the two: energy is inversely proportional to wavelength.
- Energy per mole = (energy per photon) × 6.022 × 1023.
Always convert wavelengths to meters first (1 nm = 10−9 m). Different regions of the spectrum are associated with different transitions in matter: microwaves with molecular rotation, infrared with molecular vibration, and ultraviolet and visible light with electronic transitions. The chart shows how much energy a mole of photons carries in each region, with two reference values for comparison.
Worked Example 1: Frequency, Photon Energy, and Energy per Mole for Red Light
Red light has a wavelength of 650. nm. Find its frequency, the energy of one photon, and the energy of one mole of photons.
Wavelength in meters: 650. nm = 6.50 × 10−7 m.
Frequency: ν = c/λ = (2.998 × 108) ÷ (6.50 × 10−7) = 4.61 × 1014 s−1.
Energy per photon: E = hν = (6.626 × 10−34)(4.61 × 1014) = 3.06 × 10−19 J.
Per mole: (3.06 × 10−19 J)(6.022 × 1023) = 1.84 × 105 J = 184 kJ/mol.
Worked Example 2: Finding the Wavelength That Can Break a Carbon-Carbon Bond
The C–C bond enthalpy is about 348 kJ/mol. What is the longest wavelength of light with enough energy to break one, and can 450 nm light do it?
Energy per bond: (348,000 J/mol) ÷ (6.022 × 1023) = 5.78 × 10−19 J.
Wavelength: λ = hc/E = (6.626 × 10−34)(2.998 × 108) ÷ (5.78 × 10−19) =
3.44 × 10−7 m = 344 nm, in the ultraviolet.
450 nm light: 450 nm is longer than 344 nm, so each photon carries less energy than the bond needs. Its energy per
mole is about 266 kJ/mol, below 348 kJ/mol, so no. A 300 nm photon carries about 399 kJ/mol and can.
This is why ultraviolet light, not visible light, drives photochemical reactions and damages molecules. The bond enthalpy comes from the table values used in endothermic and exothermic problems.
Worked Example 3: Finding the Longest Wavelength That Removes an Electron From Sodium
The first ionization energy of sodium is 496 kJ/mol. What is the longest wavelength of light that can remove its outer electron from a gaseous atom?
Energy per atom: 496,000 ÷ 6.022 × 1023 = 8.24 × 10−19 J.
Wavelength: λ = hc/E = (1.986 × 10−25 J·m) ÷ (8.24 × 10−19 J) = 2.41 × 10−7 m
= 241 nm.
Any light with a wavelength of 241 nm or shorter has enough energy; visible light does not, which is why sodium atoms in a lamp are not ionized by visible photons. This is the same energy balance used in photoelectron spectroscopy, where the photon energy must exceed the binding energy of the electron being removed, and it ties to ionization energy.
Worked Example 4: Ranking Radiation by Energy and Matching It to a Transition
Rank microwave (1 mm), infrared (10 µm), visible (500 nm), and ultraviolet (100 nm) radiation from lowest to highest photon energy, and name the transition each is associated with.
Energy is inversely proportional to wavelength, so the shortest wavelength has the most energy.
Microwave (about 0.12 kJ/mol) < infrared (about 12 kJ/mol) < visible (about 239 kJ/mol) <
ultraviolet (about 1200 kJ/mol).
Transitions: microwave → rotation; infrared → vibration; visible and ultraviolet → electronic transitions.
The last link is what makes spectroscopy useful. A colored solution absorbs visible light because an electronic transition matches that photon energy, and the amount absorbed gives concentration through the Beer-Lambert law.
Five Photon Energy Practice Questions With Answers
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Find the frequency of light with a wavelength of 3.00 × 10−7 m.
Show answer
ν = c/λ = 2.998 × 108 ÷ 3.00 × 10−7 = 9.99 × 1014 s−1. -
Which carries more energy per photon, red light at 700 nm or blue light at 450 nm?
Show answer
Blue light. It has the shorter wavelength, and energy is inversely proportional to wavelength. -
Which region of the spectrum is associated with molecular vibrations?
Show answer
Infrared. -
What is the energy of a photon with a frequency of 4.00 × 1014 s−1?
Show answer
E = hν = (6.626 × 10−34)(4.00 × 1014) = 2.65 × 10−19 J. -
If the wavelength of light is cut in half, what happens to the energy of each photon?
Show answer
It doubles, because energy is inversely proportional to wavelength.
Common Photon Energy Mistakes
- Leaving the wavelength in nanometers. Convert to meters before using c = λν or E = hc/λ.
- Comparing joules per photon with kJ per mole. Convert to the same units before comparing with a bond enthalpy or ionization energy.
- Treating energy as proportional to wavelength. It is inversely proportional.
- Forgetting the threshold. A photon breaks a bond or removes an electron only if its energy is at least the required value; more intensity of low-energy light does not help.
- Mixing up the regions. Infrared is vibration and ultraviolet/visible is electronic, not the reverse.
These calculations use the constants on the reference sheet. To see how a strong Unit 3 would affect your overall estimate, the AP Chem Score Calculator turns section scores into a 1–5 range.
Related Resources
- AP Chem Score Calculator
- Unit 3 Review: Properties of Substances and Mixtures
- AP Chemistry Beer-Lambert Law
- AP Chemistry Photoelectron Spectroscopy
- AP Chemistry Ionization Energy
- AP Chemistry Endothermic vs Exothermic
- AP Chemistry Reference Sheet
- AP Chemistry Study Guide
Frequently Asked Questions
What is the formula for the energy of a photon?
E = hν, where h = 6.626 × 10^-34 J·s and ν is the frequency. Because c = λν, the energy can also be written E = hc/λ. Shorter wavelength and higher frequency mean more energy per photon.
How do you convert photon energy to kJ/mol?
Multiply the energy of one photon in joules by Avogadro's number, 6.022 × 10^23, then divide by 1000 to get kJ/mol. This lets you compare a photon's energy directly with bond enthalpies and ionization energies.
Which regions of the spectrum cause which transitions?
Microwave radiation is associated with molecular rotational transitions, infrared with vibrational transitions, and ultraviolet and visible light with electronic transitions.
Can visible light break a covalent bond?
Usually not. A mole of visible-light photons carries roughly 170 to 300 kJ, which is less than the energy of most covalent bonds, such as about 348 kJ/mol for a C–C bond. Ultraviolet photons can carry enough energy.
What is the relationship between wavelength and photon energy?
They are inversely proportional: if the wavelength is halved, the energy per photon doubles.
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