PHYS116 Final Exam Review | Source: Chapter 28.2 lecture notes
Difficulty: Intermediate | Prerequisites: Photon model (E = hf), eV-to-joules conversion, and the concept of kinetic energy.
The photoelectric effect is one of the key experiments that proved light behaves as particles (photons), not just waves. It was the phenomenon Einstein explained to win his Nobel Prize. In PHYS116, this topic ties together everything from the photon model: a single photon hits a metal surface, and if it carries enough energy, it knocks an electron free. The section introduces the work function, threshold frequency, and stopping potential, all of which are standard exam material. You need to be solid on E = hf and comfortable converting between eV and joules before working through this.
When a photon hits a metal surface, it can eject an electron, but only if the photon's frequency is above a threshold set by the metal's work function. The ejected electron's maximum kinetic energy depends on the photon's frequency, not the light's intensity. Intensity only affects how many electrons are ejected per second, not how fast each one leaves.
Photoelectric effect
The emission of electrons from a metal surface when light of sufficient frequency shines on it. Think of it as a photon spending its energy to prise an electron out of the metal.
Work function (E₀)
The minimum energy a photon must deliver to free an electron from a particular metal surface, measured in eV. Each metal has its own value (e.g., potassium 2.30 eV, gold 5.10 eV). In simple terms, it is the "entry fee" the photon has to pay.
Threshold frequency (f₀)
The minimum frequency of light that can eject an electron from a given metal: f₀ = E₀ / h. Below this frequency, no electrons are emitted regardless of how bright the light is.
Maximum kinetic energy (K_max)
The greatest kinetic energy an ejected electron can have: K_max = hf - E₀. The electron that loses the least energy escaping the surface leaves with K_max.
Stopping potential (V_stop)
The reverse voltage needed to stop the fastest ejected electrons from reaching the anode: V_stop = K_max / e. Measuring V_stop tells you K_max directly.
Cathode
The metal surface that emits electrons when illuminated.
Anode
The electrode that collects the ejected electrons. Making it positive attracts all electrons; making it negative repels them, and at V_stop even the fastest ones are turned back.
Light (photons) hits a metal cathode. Each photon interacts with one electron.
The photon's full energy (E_photon = hf) is absorbed by the electron.
The electron uses some of that energy to escape the metal (this costs at least E₀, the work function). Whatever energy is left over becomes the electron's kinetic energy.
Energy balance: KE = E_photon - ΔE, where ΔE is the energy lost escaping. The minimum loss is E₀ (for surface electrons), so the maximum KE is:
K_max = hf - E₀
Electrons are emitted only if f > f₀, where f₀ = E₀ / h.
Below the threshold frequency, no electrons are emitted no matter how intense the light. This is because each individual photon lacks enough energy to free an electron.
By applying a negative voltage to the anode, you can repel ejected electrons back toward the cathode.
The voltage at which even the fastest electron is stopped is V_stop = K_max / e.
Measuring V_stop is the experimental method for determining K_max.
The stopping potential does not depend on the intensity of the light. It depends only on the frequency of the light and the work function of the metal.
Frequency determines the energy per photon, and therefore whether electrons are emitted and how much kinetic energy they have.
Intensity determines the number of photons per second, and therefore how many electrons are ejected per second (the photocurrent).
Doubling the intensity doubles the number of ejected electrons but does not change K_max or V_stop.
Potassium: 2.30 eV
Sodium: 2.75 eV
Aluminium: 4.28 eV
Tungsten: 4.55 eV
Copper: 4.65 eV
Iron: 4.70 eV
Gold: 5.10 eV
Metals with lower work functions (potassium, sodium) emit electrons more easily and have lower threshold frequencies.
Photon energy
E_photon = hf
Maximum kinetic energy of ejected electron
K_max = hf - E₀
Threshold frequency
f₀ = E₀ / h
Stopping potential
V_stop = K_max / e = (hf - E₀) / e
Key constants
h = 6.63 × 10⁻³⁴ J·s, e = 1.60 × 10⁻¹⁹ C, 1 eV = 1.60 × 10⁻¹⁹ J
The photoelectric effect is the operating principle behind solar cells: photons from sunlight eject electrons in semiconductor material, generating an electric current. It also underpins light sensors in cameras, automatic doors, and smoke detectors, where incoming photons trigger an electronic signal.
Students often think that brighter light will eject faster electrons. It will not. Intensity affects the number of electrons ejected, not their speed. Only frequency determines K_max.
A common error is thinking that any light, if bright enough, can eject electrons. Below the threshold frequency, no electrons are emitted regardless of intensity, because no single photon has enough energy.
Students sometimes confuse the work function with the kinetic energy of the ejected electron. The work function is the energy cost of escape; the kinetic energy is what is left over after that cost is paid.
When computing V_stop, students occasionally forget to divide K_max by e (the elementary charge), leaving the answer in joules rather than volts.
⚠️ The distinction between intensity and frequency is heavily tested. Be ready to explain why doubling intensity doubles the photocurrent but leaves V_stop unchanged.
⚠️ Expect problems that give a photon wavelength and a metal's work function and ask for K_max and V_stop.
⚠️ Know the threshold frequency formula f₀ = E₀/h and be able to determine whether a given wavelength of light will cause emission for a specific metal.
⚠️ Work function tables appear on exams. You may need to identify which metals will emit electrons under a given light source.
True or false: Increasing the intensity of light above the threshold frequency increases the maximum kinetic energy of ejected electrons. False. Intensity increases the number of electrons, not their maximum KE.
Fill in the blank: The threshold frequency for a metal with work function 2.30 eV is f₀ = ______. f₀ = E₀/h = (2.30 × 1.60 × 10⁻¹⁹) / (6.63 × 10⁻³⁴) = 5.55 × 10¹⁴ Hz
True or false: Red light (f ≈ 4.3 × 10¹⁴ Hz) can eject electrons from gold (E₀ = 5.10 eV). False. The threshold frequency for gold is about 1.23 × 10¹⁵ Hz, well above the frequency of red light.
True or false: The stopping potential depends on the intensity of the incident light. False. It depends only on frequency and work function.
Fill in the blank: K_max = ______ - ______. hf - E₀
Q: Ultraviolet light with a wavelength of 250 nm hits a sodium surface (E₀ = 2.75 eV). What is the maximum kinetic energy of the ejected electrons?
A: f = c/λ = (3.00 × 10⁸) / (250 × 10⁻⁹) = 1.20 × 10¹⁵ Hz. E_photon = hf = (6.63 × 10⁻³⁴)(1.20 × 10¹⁵) = 7.96 × 10⁻¹⁹ J = 4.97 eV. K_max = 4.97 - 2.75 = 2.22 eV.
Q: What is the stopping potential for the electrons in the previous problem?
A: V_stop = K_max / e = 2.22 eV / e = 2.22 V.
Q: Light of frequency 5.0 × 10¹⁴ Hz shines on potassium (E₀ = 2.30 eV). Are electrons emitted? If so, what is K_max?
A: E_photon = hf = (6.63 × 10⁻³⁴)(5.0 × 10¹⁴) = 3.32 × 10⁻¹⁹ J = 2.07 eV. Since 2.07 eV < 2.30 eV, no electrons are emitted. The photon energy is below the work function.
Q: If you double the intensity of the light in the previous problem, will electrons now be emitted?
A: No. Doubling intensity doubles the number of photons but does not change each photon's energy. Each photon still has only 2.07 eV, which is below the 2.30 eV work function.
This connects directly to the photon model (Ch. 25.6), which provides the framework (E = hf) that makes the photoelectric effect explicable. Without quantised photon energy, classical wave theory predicts that any light, given enough time, should eject electrons, which is exactly what experiments showed does not happen.
It also connects to the EM spectrum (Ch. 25.7): knowing where a given light source sits on the spectrum tells you its photon energy, which determines whether it can overcome a given metal's work function.
Looking ahead, the photoelectric effect is foundational to quantum mechanics and the broader idea of wave-particle duality.
Tags: photoelectric effect, work function, threshold frequency, stopping potential, K_max, maximum kinetic energy, photon energy, E = hf, cathode, anode, electron emission, photocurrent, intensity vs frequency, Planck's constant, electronvolt, eV, potassium, sodium, gold, copper, Einstein, wave-particle duality, PHYS116, general physics, University of Washington, Chapter 28.2