This unit shows that light carries energy in separate packets called photons, even though it also travels and interferes like a wave. By the end, you should be able to calculate photon energy and momentum, solve photoelectric effect problems, and explain which experiments reveal light's wave side and which reveal its particle side.
Read the overview first, then work through each topic's notes and try the checkpoint question before checking the answer.
Classical physics treated light as a smooth, continuous wave, and around 1900 that picture started making wrong predictions. This unit follows the fix, from Planck's quanta to Einstein's photons to the idea that light has both wave and particle behavior. The math is mostly one equation, , used in a few different ways.
Honors Physics Unit 21 covers the quantum model of light. You learn how Max Planck modeled blackbody radiation in 1900 using oscillator energies in multiples of , how Albert Einstein used photons in 1905 to explain the photoelectric effect with , and how experiments like the double slit and Compton scattering show that light acts as both a wave and a particle. You should be able to convert between wavelength, frequency, and photon energy, work in joules and electron volts, find threshold frequency and stopping potential, and calculate photon momentum with . Some schools place this unit near the end of the course or combine it with atomic and nuclear physics.
Planck assigned his model oscillators energies in multiples of , with J·s. A photon of frequency has energy . Higher frequency means a bigger packet. That one assumption fixed the blackbody prediction that classical physics got wrong.
In the single-photon model of the photoelectric effect, one electron absorbs one photon. If is less than the work function, that photon cannot eject an electron. At fixed frequency above the threshold, greater intensity generally ejects more electrons per second without changing their maximum kinetic energy. At very high intensities, an electron can absorb multiple photons.
Interference and diffraction reveal wave behavior. The photoelectric effect and Compton scattering reveal energy and momentum transfer by photons. A quantum description accounts for both kinds of behavior.
Frequency is a wave property, and energy per photon is a particle property, and connects them directly. This equation is useful for many calculations in this unit. Once you have a photon's energy, you can compare it to a work function, find an electron's kinetic energy, or get the photon's momentum from .
Light energy comes in chunks.
When light of high enough frequency hits a metal, electrons fly off.
Light acts as a wave in some experiments and as a particle in others, and you need both descriptions.
Light energy comes in chunks. A blackbody is an ideal object whose glow depends only on its temperature, which is why a heated stove coil goes from dull red to orange as it gets hotter. Classical wave theory predicted that a hot object should give off unlimited energy at ultraviolet frequencies, a failed prediction called the ultraviolet catastrophe.
In 1900, Max Planck modeled the radiation by assigning his oscillators energies in whole-number multiples of . The energy step is one quantum. High-frequency quanta cost so much energy that hot objects rarely emit them, so the predicted curve drops back down at short wavelengths, matching experiments.
Using the wavelength in vacuum, , so you can also write . In a material, use the wave speed in that material to relate wavelength and frequency. Shorter wavelength means more energy per photon, so one UV photon carries more energy than one red photon. The same idea explains spectral lines, since atoms emit photons whose energy exactly matches the gap between fixed energy levels.
Worked example. A green laser emits 532 nm light. First, Hz. Then J, which is about 2.33 eV. A 5.0 mW laser emits photons every second.
Which photon has more energy, one with wavelength 400 nm or one with wavelength 700 nm, and by what factor? (Answer: The 400 nm photon, because , so it has 700/400 = 1.75 times as much energy.)
When light of high enough frequency hits a metal, electrons fly off. In 1887, Heinrich Hertz observed that ultraviolet light affected electric sparks. In 1905, Einstein explained photoelectric emission by proposing light quanta, now called photons, each with energy . In the single-photon model, one electron absorbs one photon. The work function is the minimum energy needed to free an electron. An electron that escapes without other energy losses has maximum kinetic energy:
In the single-photon model, if , one photon cannot eject an electron. At very high intensities, multiphoton absorption can cause emission below this threshold. The threshold frequency is . At fixed frequency above the threshold, raising intensity generally increases the number of emitted electrons per second without changing . For frequencies that produce emission, a graph of versus is a straight line with slope and an x-intercept at .
In the lab, you measure with the stopping potential , the reverse voltage that just stops the fastest electrons, using .
Worked example. Light of wavelength 200 nm hits a metal with eV. Using eV·nm, the photon energy is eV. Since 6.20 eV is greater than 4.50 eV, electrons are ejected with eV, or J. The stopping potential is 1.70 V.
You double the intensity of light that is already above the threshold frequency. What happens to the number of ejected electrons and to ? (Answer: The number of electrons per second roughly doubles, but does not change because each photon still has the same energy .)
| Observation | Classical wave prediction | Photon model prediction | What experiments show |
|---|---|---|---|
| Brighter light | Faster electrons | More electrons, same maximum speed | More electrons, same maximum speed |
| Very dim light above threshold | Delay while energy builds up | Electrons come out right away | Electrons come out right away |
| Bright light below threshold | Electrons eventually ejected | No electrons ever | No electrons ever |
| Higher frequency | No universal threshold or linear relation for $K_{max}$ | Higher $K_{max}$, rising linearly | Higher $K_{max}$, rising linearly |
Light acts as a wave in some experiments and as a particle in others, and you need both descriptions. In a double-slit experiment, light produces bright and dark bands through constructive and destructive interference. The photoelectric effect and Compton scattering show energy and momentum transfer by photons. A quantum description accounts for both kinds of observation.
Photons have zero rest mass, but they still carry momentum. In this formula, is the wavelength in vacuum:
Shorter wavelength means more momentum. That push is what lets a solar sail accelerate in space with no fuel.
In 1923, Arthur Compton fired X-rays at electrons and found the scattered X-rays had longer wavelengths. The photon behaved like a billiard ball, giving some energy and momentum to the electron. For a free electron initially at rest, the shift is , where is the photon's scattering angle and m. The shift is zero at and largest (twice that value) at .
Louis de Broglie flipped the idea in 1924, proposing that matter also has a wavelength, . Electrons do form interference patterns, so duality applies to matter too.
Worked example. A 500 nm photon has momentum kg·m/s. Each photon gives a tiny push, but many photons together exert a continuous force on a solar sail.
For Compton scattering from a free electron initially at rest, at what angle is the wavelength shift largest, and how big is it? (Answer: At , where , so the shift is m.)
| Experiment | What you observe | Model that explains it |
|---|---|---|
| Double slit | Alternating bright and dark bands | Wave (interference) |
| Single slit or edge | Light spreads into the shadow region | Wave (diffraction) |
| Photoelectric effect | Threshold frequency, instant emission | Particle (photons with energy $hf$) |
| Compton scattering | Longer wavelength after scattering, depends on angle | Particle (photons with momentum $h/\lambda$) |
| Term | Definition |
|---|---|
| Photon | A quantum of electromagnetic energy with energy $E = hf$ and momentum $p = h/\lambda$, where $\lambda$ is its wavelength in vacuum. |
| Planck's constant | The constant $h = 6.63 \times 10^{-34}$ J·s that links a photon's frequency to its energy. |
| Blackbody radiation | The spectrum of light given off by an ideal object, which depends only on the object's temperature. |
| Photoelectric effect | The ejection of electrons from a metal when light above a threshold frequency shines on it. |
| Work function | The minimum energy needed to remove an electron from a metal surface, written $\phi$. |
| Threshold frequency | The lowest frequency of light that can eject electrons from a given metal, equal to $\phi/h$. |
| Stopping potential | The reverse voltage that just stops the fastest photoelectrons, related by $eV_s = K_{max}$. |
| Compton effect | The lengthening of a photon's wavelength when it scatters off a free electron initially at rest. The shift is explained using photon energy and momentum. |
| Wave-particle duality | The principle that light and matter show wave behavior in some experiments and particle behavior in others. |
| de Broglie wavelength | The wavelength of a moving particle, given by $\lambda = h/p$. |
In everyday life, brighter usually means more energy, so this feels natural. At fixed frequency and illuminated area, greater intensity means more photons arrive per second. In the single-photon model, each absorbed photon has energy , so raising intensity does not raise .
Work functions are usually given in eV, while J·s gives photon energy in joules when multiplied by frequency in hertz. Convert the energies to matching units before subtracting. Pick one unit system and convert with J, and change nanometers to meters by multiplying by . A handy shortcut is eV·nm.
The formula applies to massive objects moving much slower than light. It cannot be used for photons. Light carries momentum , which is why Compton scattering conserves momentum and why solar sails work.
Light doesn't change its nature mid-flight. It has both properties all the time, and the experiment you set up determines which one shows up. Interference experiments reveal the wave behavior, and energy-transfer experiments like the photoelectric effect reveal the particle behavior.