HS-PS4-3: Evaluating the Wave and Particle Models of Light
In plain English: HS-PS4-3 is the NGSS high school performance expectation that asks students to evaluate the claims, evidence and reasoning behind describing electromagnetic radiation with a wave model or a particle model. Students weigh evidence from interference, diffraction, resonance and the photoelectric effect and decide which model is more useful in a given situation. It is usually taught in Physics.
Evaluate the claims, evidence, and reasoning behind the idea that electromagnetic radiation can be described either by a wave model or a particle model, and that for some situations one model is more useful than the other.
Clarification Statement: Emphasis is on how the experimental evidence supports the claim and how a theory is generally modified in light of new evidence. Examples of a phenomenon could include resonance, interference, diffraction, and photoelectric effect.
Assessment Boundary: Assessment does not include using quantum theory.
Next Generation Science Standards · Disciplinary Core Idea: Waves and Their Applications in Technologies for Information Transfer · Official standard
For three centuries scientists argued about whether light is a stream of particles or a wave, and the evidence kept changing the answer. In this lesson students act as the judges. They evaluate claims, the evidence offered for them and the reasoning that links the two, using phenomena they can measure or analyze: interference and diffraction of laser light, resonance in a microwave oven, and data from the photoelectric effect. They find that interference, diffraction and resonance make sense only with a wave model, that the photoelectric effect and the detection of very faint light fit a model of separate packets of energy, and that physicists today use whichever model is more useful for the situation. Students also trace how the model of light was modified as new evidence arrived, from Newton to Einstein and Millikan.
The NGSS Clarification Statement says: "Emphasis is on how the experimental evidence supports the claim and how a theory is generally modified in light of new evidence. Examples of a phenomenon could include resonance, interference, diffraction, and photoelectric effect." The Assessment Boundary says: "Assessment does not include using quantum theory." This lesson therefore uses the particle model only in words (light delivers energy in packets, and the energy per packet is larger for higher frequencies); the photon-energy equation and any calculation with Planck's constant are beyond this standard. The calculations on the page use wave relations (c = fλ, fringe spacing) and energy = power × time. All data sets are invented for teaching and labeled as invented, with values that match real materials.
Learning Objectives
By the end of this lesson, students will be able to:
Explain how interference, diffraction and resonance provide evidence for a wave model of electromagnetic radiation, and use c = fλ and the fringe spacing λL/d with data
Explain how photoelectric data (a threshold frequency, no delay, electron energy that does not depend on brightness) provide evidence for a particle model
Evaluate a claim-evidence-reasoning argument about light, identifying evidence that fits both models and reasoning that does not follow
Decide which model is more useful for a given situation and justify the choice with evidence
Describe how the model of light was modified as new evidence appeared
Prior Knowledge Required
Students should already be comfortable with:
Waves are reflected, absorbed or transmitted by materials MS-PS4-2
The relationship among wave speed, frequency and wavelength, v = fλ HS-PS4-1
Energy transferred equals power multiplied by time, with units of joules and watts
Scientific notation and unit conversions between nm, mm and m HSN.Q.A.1
Shine a class 2 laser pointer through a narrow single slit onto the wall, first with a wide slit and then with a very narrow one. (Safety: never point the laser at anyone, and keep it below eye level.)
Warm-Up Prompt
"When the slit got narrower, the spot on the wall got wider, not narrower. If light were a stream of tiny balls flying in straight lines, what should have happened? Write one claim about what light is and the evidence you just saw."
Share two or three claims. Many students expect a narrower slit to make a narrower spot. Record the claims on the board; they are the first arguments the class will evaluate.
Direct Instruction15-20 minutes
Two models, one kind of radiation. In the wave model, electromagnetic radiation is an oscillating electric and magnetic field that spreads out, with speed c = fλ. Waves from two sources add: where crests meet crests the light is bright, and where crests meet troughs it cancels (interference). Waves bend around edges and spread after passing through an opening comparable to their wavelength (diffraction), and waves can form standing patterns in a cavity whose size fits the wavelength (resonance). In the particle model, light delivers its energy in separate packets (photons). Each packet is absorbed all at once, and the energy of one packet is larger for higher frequencies; the equation for that energy is part of quantum theory and beyond this standard. Evaluate each piece of evidence by asking: which model predicted it, and could the other model explain it at all?
Interference (wave evidence)
A green laser (532 nm) shines on two slits 0.20 mm apart. On a screen 1.50 m away, students measure bright fringes 4.0 mm apart (Diagram 1).
Result: Wave model: spacing = λL/d = (532 × 10⁻⁹ m)(1.50 m) ÷ (0.20 × 10⁻³ m) = 3.99 × 10⁻³ m ≈ 4.0 mm. Working backward, 4.0 mm gives λ ≈ 533 nm. Particles moving in straight lines would give two bright strips, not a row of evenly spaced fringes with dark gaps.
Diffraction grating (wave evidence)
A red laser (650 nm) passes through a grating with 500 lines per mm. Where should the first bright spot beside the center appear?
Result: d = 1/500 mm = 2.0 × 10⁻⁶ m. sin θ = λ/d = 650 × 10⁻⁹ ÷ 2.0 × 10⁻⁶ = 0.325, so θ ≈ 19.0°. The measured angle matches the wave prediction, and a grating works only because waves from many slits interfere.
Photoelectric timing (particle evidence)
Dim light of intensity 0.010 W/m² falls on sodium. An electron needs about 2.3 eV (3.68 × 10⁻¹⁹ J) to escape. Suppose, as the wave model does, that each atom collects the energy spread over an area of about 1.0 × 10⁻¹⁹ m².
Result: Power per atom = 0.010 × 1.0 × 10⁻¹⁹ = 1.0 × 10⁻²¹ W, so t = 3.68 × 10⁻¹⁹ J ÷ 1.0 × 10⁻²¹ W ≈ 368 s, about 6 minutes. Experiments find no measurable delay (less than about a billionth of a second). The wave prediction fails; energy arriving in packets explains it.
Photoelectric data (particle evidence)
Invented data for a sodium plate: stopping voltage 0.20, 0.62, 1.03, 1.44 and 1.86 V for light of 6.0, 7.0, 8.0, 9.0 and 10.0 × 10¹⁴ Hz. The same values appear with a lamp four times brighter. Below 5.5 × 10¹⁴ Hz no electrons leave the plate at all (Diagram 2).
Result: The best-fit line rises 0.414 V per 10¹⁴ Hz and crosses zero at about 5.5 × 10¹⁴ Hz, the threshold. The wave model predicts that brighter light gives electrons more energy and that any frequency works if you wait; the data show neither. (What the slope means requires quantum theory, beyond this standard.)
Light in water (a theory modified)
Newton's particle model explained refraction by saying light speeds up when it enters water. The wave model says it slows down. Water bends light by a factor of 1.33 (its index of refraction).
Result: Wave prediction: v = c ÷ 1.33 = 3.00 × 10⁸ ÷ 1.33 ≈ 2.26 × 10⁸ m/s. Newton's prediction: v = 1.33c ≈ 3.99 × 10⁸ m/s. Foucault measured in 1850 that light is slower in water, which ruled out Newton's version of the particle model and strengthened the wave model for the rest of the 1800s.
After the examples, draw a two-column evidence chart (wave, particle) on the board and let students place each example. Point out that the last example did not end the debate: it rejected one particle model, and new evidence (the photoelectric effect) later brought a different particle model back.
Guided Practice15 minutes
Pairs decide which model is more useful in each situation, then write the evidence that justifies the choice. Discuss as a class; the point is not that one model is "true" but that each is the better tool for some jobs.
Which model is more useful here?
Situation
More useful model
Why
Predicting where the bright spots fall when a laser passes through two slits
Wave
Fringe positions come from path differences of a whole number of wavelengths
Explaining why ultraviolet light, but not visible light, knocks electrons out of zinc
Particle
Only packets above a threshold frequency carry enough energy to free one electron
Choosing the length of a car radio antenna
Wave
The antenna resonates when its length fits the wavelength
Explaining the colors on the surface of a DVD
Wave
Closely spaced tracks act as a diffraction grating
Explaining why electrons leave a metal at once even in very dim light
Particle
Each packet delivers its energy to one electron at a time, with no build-up needed
For each row, name the phenomenon (interference, diffraction, resonance or photoelectric effect).
Write what the other model would predict, and say whether the evidence rules it out or just makes it less convenient.
Add one situation of your own to the table and trade with another pair.
Independent Practice10-15 minutes
Each student evaluates this argument: "Claim: light is made of particles. Evidence: light travels in straight lines, which is why shadows have sharp edges. Reasoning: waves always bend around objects, so they could not make sharp shadows." Students use invented data from the warm-up setup: a red laser (650 nm) passes through single slits of different widths onto a screen 2.0 m away.
Independent practice data (invented): width of the central bright band
Slit width a (mm)
Measured width of central band (mm)
0.50
5.3
0.20
12.9
0.10
26.2
Students compare each measurement with the wave prediction 2λL/a (5.2, 13 and 26 mm), then judge the argument: the evidence is real, but sharp shadows fit both models because everyday objects are thousands of times wider than the wavelength of light, and the reasoning is false because the spreading depends on the size of the opening. They finish by rewriting the argument so that its claim matches all of the evidence.
Closure5 minutes
Exit ticket: "Name one phenomenon for which the wave model is more useful and one for which the particle model is more useful. For each, give the piece of evidence that the other model cannot explain." Revisit the warm-up claims and ask students which ones they would now revise, and why.
Differentiation Strategies
For Struggling Students
Give a claim-evidence-reasoning organizer with the three parts in separate boxes and a question under each ("Does the evidence fit both models?")
Use a ripple tank video or water waves in a tray to show interference before moving to light
Provide a unit card for nm, μm, mm and m with worked conversions, and let students use it on every wave calculation
For Advanced Students
Ask students to research how G. I. Taylor's 1909 experiment with extremely faint light produced the same diffraction pattern as bright light, and argue what it shows about both models
Have students estimate how the wave-model delay for the photoelectric effect changes if an atom could collect energy from a larger area, and judge whether any reasonable area rescues the wave model
Ask students to write the argument a scientist in 1900 would have made for the wave model and a reply from 1916 using Millikan's results
Assessment Guidance
What to Look For
Check that students tie each model to specific evidence instead of saying "light is both" without support. Look for arguments that notice when evidence fits both models (reflection, straight-line travel) and so cannot decide between them. Listen for the misconception that brighter light gives photoelectrons more energy, and for students who think the photoelectric effect disproved the wave model entirely. Strong answers describe how the model changed when new evidence arrived and stay away from quantum calculations, which are beyond this standard.
02
Classroom Activities
3 Activities
1
Resonance in a Microwave Oven: Measuring the Speed of Light
20 minWhole class, then pairs
Microwaves form a standing wave inside the metal box of a microwave oven, so some spots get much hotter than others. With the turntable removed, a flat bar of chocolate melts first at the hot spots, which are half a wavelength apart. Pairs measure the spacing and use c = fλ with the oven's frequency (2.45 GHz, printed on the label) to find the speed of the waves.
Procedure
The teacher removes the turntable, places the chocolate on a microwave-safe plate that does not rotate, and heats it for about 15-20 s, checking after each short run until 3-5 soft spots appear.
Pairs measure the distance between neighboring melted spots with a ruler, in centimeters, and record at least four spacings.
Compute λ = 2 × (spacing) and c = fλ.
Safety: only the teacher operates the oven; no metal inside; never run the oven empty; the plate may be hot; lab food is not eaten.
Sample Data (invented)
Spacings between melted spots: 6.0, 6.3, 6.1 and 6.2 cm. Mean spacing 6.15 cm, so λ = 12.3 cm and c = (2.45 × 10⁹ Hz)(0.123 m) ≈ 3.01 × 10⁸ m/s, within 1% of the accepted value.
Discussion Questions
Resonance appears only when the box size fits a whole number of half wavelengths. Which model of light predicts hot spots at a fixed spacing, and why can the particle model not explain them on its own?
Why does the oven normally use a turntable?
If the class result were 10% too high, which measurement would you suspect first, and how would you test it?
Modification for Distance Learning
Students watch a video of the chocolate test with a ruler in view, measure the spacings from the video, and post their calculation of c to the class board.
2
Glow-in-the-Dark Threshold Lab
25 minGroups of 3
Glow-in-the-dark sheets store energy from light and release it slowly. Groups charge small spots with red, green, blue and UV LED flashlights and compare the glow in the dark. They then try to charge the sheet with red light that is brighter and shines longer, and decide which model of light the results support.
Procedure
Keep the sheet in a dark box for 10 minutes so it stops glowing. Mark four spots.
Shine each flashlight on its own spot for 10 s from 5 cm away. Close the box and rate each spot's glow from 0 (none) to 5 (brightest), or read a phone light-meter app held against a hole in the box.
Recharge a new spot with red light for 60 s, then with two red flashlights together for 60 s.
Safety: wear UV-blocking safety glasses, never look into the UV flashlight, and point all flashlights down at the sheet.
Sample Data (invented)
Glow rating after 10 s: red 0, green 1, blue 4, UV 5. Red for 60 s: 0. Two red flashlights for 60 s: 0.
Discussion Questions
In the wave model, the energy delivered is power × time, so enough red light for long enough should charge the sheet. Do the data support that prediction?
The red light never charged the sheet, even brighter and longer, while a short flash of UV did. How does a model of energy packets, with more energy per packet at higher frequency, explain this?
Which phenomenon in this lesson shows the same pattern of a threshold that brightness cannot overcome?
Challenge Variation
Groups test a yellow or orange LED and predict, before testing, whether it will charge the sheet. They explain their prediction with the particle model and report whether the evidence supported it.
3
Model Court: Evaluating Arguments and the History of Evidence
25 minGroups of 4
Groups receive six evidence cards from the history of light and three argument cards. First they place the evidence cards on a timeline and mark which model each one supported. Then they act as judges: for each argument card they rule whether the claim, the evidence and the reasoning hold up.
Evidence Cards
Newton, Opticks (1704): light as a stream of particles, which explains straight-line travel and, he argued, refraction.
Thomas Young, early 1800s: light through two slits makes bright and dark fringes.
Foucault, 1850: light travels more slowly in water than in air.
Hertz, 1887: while producing radio waves, he noticed that ultraviolet light helps sparks jump a gap.
Lenard, 1902: the energy of electrons knocked out of a metal depends on the frequency of the light, not its brightness.
Millikan, 1916: careful stopping-voltage measurements match Einstein's 1905 prediction that light energy arrives in packets.
Argument Cards
A. "Light is a wave, because it reflects off mirrors."
B. "The photoelectric effect proves the wave model was wrong, so scientists threw it away in 1905."
C. "Light behaves as a wave when it spreads and interferes, because only waves make fringes, and as packets when it is absorbed, because a threshold frequency exists that no brightness can overcome. Each model is more useful for different situations."
Teacher key: C is the strong argument. A uses evidence that both models explain. B has false reasoning and false history: the wave model is still used for interference, diffraction and radio.
Discussion Questions
Which evidence card rejected one version of the particle model, and which later cards supported a different one?
The same experiments in which Hertz produced radio waves also first noticed the photoelectric effect. What does this show about how evidence for two different models can appear together?
Rewrite argument A so that its evidence can actually tell the two models apart.
Modification for Distance Learning
Put the cards on a shared slide deck. Groups drag the evidence cards onto a timeline and record their ruling on each argument in a comment.
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: Two-Slit Interference Pattern (Wave Model Prediction)
Brightness on a screen 1.50 m behind two slits 0.20 mm apart, lit by 532 nm laser light, computed from the wave model and drawn to scale. Bright fringes (dots) repeat every λL/d ≈ 4.0 mm, and the light cancels completely between them. A model of particles moving in straight lines predicts no dark gaps, so the pattern is evidence for the wave model.
Diagram 2: Photoelectric Data for Sodium (Particle Model Evidence)
Invented data for a sodium plate, drawn to scale. Stopping voltage (a measure of the fastest electrons' energy) rises in a straight line with frequency, starting at a threshold of about 5.5 × 10¹⁴ Hz. A lamp four times brighter gives the same values, and light below the threshold ejects no electrons at any brightness. The wave model predicted the opposite on both points.
04
Homework Assignment
~30 min
HS-PS4-3 Homework: Wave Evidence, Particle Evidence and Choosing a Model
Directions: Data sets are invented for practice, with values that match real materials. Use c = 3.00 × 10⁸ m/s and 1 eV = 1.602 × 10⁻¹⁹ J. Show units in every calculation. Where a problem asks you to evaluate an argument, judge its claim, its evidence and its reasoning separately. Calculations with Planck's constant are not needed and are beyond this standard.
Part 1: Evidence for the Wave Model (Problems 1-2)
A laser of unknown color shines through two slits 0.30 mm apart onto a screen 2.50 m away. Six bright fringes in a row span 22.5 mm from the first to the sixth. (a) Find the fringe spacing. (b) Find the wavelength in nm and name its approximate color. (c) Evaluate the claim "These fringes prove that light is only a wave."
An FM station broadcasts at 98.5 MHz. (a) Find the wavelength of its radio waves. (b) A simple antenna resonates best when its length is about half a wavelength. Find that length. (c) Explain whether the wave model or the particle model is more useful for designing the antenna, and what evidence supports your choice.
Part 2: Evidence for the Particle Model (Problems 3-4)
Invented data for a calcium plate: stopping voltages of 0.44, 0.85, 1.27 and 1.68 V for light of 8.0, 9.0, 10.0 and 11.0 × 10¹⁴ Hz. (a) Graph the data and draw a best-fit line. (b) Use the line to estimate the threshold frequency. (c) Predict what happens when a very bright lamp at 6.0 × 10¹⁴ Hz shines on the plate, and state which model predicts this correctly. (d) Compare the threshold with the sodium threshold in Diagram 2 and describe what the difference means for which colors can free electrons from each metal.
Light of intensity 5.0 × 10⁻³ W/m² falls on the calcium plate, whose electrons need about 2.9 eV to escape. (a) Convert 2.9 eV to joules. (b) Using the wave model, and assuming each atom collects energy over an area of 2.0 × 10⁻¹⁹ m², estimate how long an electron must wait before it can escape. (c) Electrons are observed to leave within a billionth of a second. Which claim does this support? (d) A defender of the wave model questions the area assumption. Evaluate this reply: how large would the collecting area need to be for a delay of 10⁻⁹ s, and is that reasonable for one atom?
Part 3: Choosing and Revising Models (Problems 5-6)
Newton's particle model predicted that light moves faster in glass than in air, and the wave model predicted that it moves slower. For glass, the index of refraction is 1.50. (a) Find the speed of light in glass predicted by each model. (b) Measurements give about 2.0 × 10⁸ m/s. Which prediction does the evidence support? (c) Explain why this evidence rejected Newton's model but did not rule out every possible particle model.
For each situation, decide whether the wave model or the particle model is more useful and write a one-sentence justification that names the evidence: (a) the colored bands on a thin film of oil floating on a puddle; (b) a red safelight in a photography darkroom that does not expose black-and-white photo paper, however long it stays on; (c) the pattern of light that spreads behind a narrow gap in a curtain. Then write a short claim-evidence-reasoning paragraph that answers the question "Is light a wave or a particle?"
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
Wave Calculations
Fringe spacing, wavelength and antenna length correct with units and conversions
Correct method with one unit or conversion error
Analyzing Photoelectric Data
Threshold found from the graph and brightness and delay results linked to the correct model
Threshold found, but the link to a model is missing or unclear
Evaluating Arguments
Claim, evidence and reasoning judged separately, with evidence that fits both models identified
Argument judged as a whole without separating its parts
Choosing a Model
Each choice justified by a specific phenomenon and a statement of how theories change with evidence
Choices correct but justified only in general terms
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Data sets are invented, with values that match real materials. Use c = 3.00 × 10⁸ m/s. No question needs Planck's constant or quantum theory. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
Which observation is the strongest evidence for the wave model of light?
Answer: C
Dark bands appear where waves from the two slits arrive crest to trough and cancel, which only a wave model predicts. Choices A and B are explained by both models, so they cannot decide between them. Choice D is also explained by both models, since waves and particles can both carry energy.
Question 2 of 20 · Multiple Choice
Which observation is the strongest evidence for the particle model of light?
Answer: A
Brightness cannot make up for a low frequency, which fits energy delivered in packets whose size depends on frequency: each orange packet carries too little energy, however many arrive. Choice B is explained by both models (and the measured speed in water favors waves). Choices C and D are resonance and diffraction, which are wave evidence.
Question 3 of 20 · Multiple Choice
Red laser light passes through two slits 0.18 mm apart, and bright fringes 4.2 mm apart appear on a screen 1.20 m away. What is the wavelength?
Answer: B
λ = (fringe spacing)(d) ÷ L = (4.2 × 10⁻³ m)(0.18 × 10⁻³ m) ÷ 1.20 m = 6.3 × 10⁻⁷ m = 630 nm, a red wavelength. Choice A doubles the spacing, as if 4.2 mm were the distance from a bright fringe to the next dark one (half a spacing). Choice C halves it, as if 4.2 mm covered two fringe spacings. Choice D is off by a factor of ten from a conversion error.
Question 4 of 20 · Multiple Choice
In a two-slit experiment, the slits are moved so that they are half as far apart. According to the wave model, what happens to the fringe spacing on the screen?
Answer: D
The spacing is λL/d, so halving d doubles it. Choice A reverses the relationship. Choice C squares the factor, which the formula does not support, and choice B ignores d.
Question 5 of 20 · Multiple Choice
Invented data: light of 7.5 × 10¹⁴ Hz shines on a sodium plate at three brightness settings, 1, 2 and 3. The current is 0.4, 0.8 and 1.2 μA, and the stopping voltage is 0.82 V every time. What do the data show?
Answer: B
The current triples with brightness, so more electrons leave each second, while the unchanged stopping voltage shows that the most energetic electrons are no more energetic. Choice A is the wave-model prediction the data contradict. Choice C ignores the current. Choice D is impossible because electrons are leaving the plate.
Question 6 of 20 · Multiple Choice
Before 1905, the wave model made a prediction about very dim light shining on a metal. Which prediction did experiments show to be wrong?
Answer: C
In the wave model, energy spreads evenly over the wavefront, so an electron would need time to collect enough, and any frequency would do if you waited. Experiments show no measurable delay and a firm threshold frequency. Choices A, B and D are not predictions of the wave model at all: faint light still interferes and travels at the same speed.
Question 7 of 20 · Multiple Choice
A student heats chocolate in a microwave oven without its turntable. The melted spots are 6.0 cm apart, and the oven runs at 2.45 GHz. What speed of the waves do these data give?
Answer: A
Hot spots of a standing wave are half a wavelength apart, so λ = 12 cm = 0.12 m and c = fλ = (2.45 × 10⁹ Hz)(0.12 m) = 2.94 × 10⁸ m/s. Choice B uses the spot spacing as the whole wavelength. Choice C uses four times the spacing as the wavelength, and choice D uses the 6.0 cm spacing as the whole wavelength and also leaves it in centimeters (2.45 × 10⁹ × 6.0).
Question 8 of 20 · Multiple Choice
A student argues: "Light must be made of particles, because it crosses the empty space between the Sun and Earth, and waves need a material to travel through." What is the best evaluation of this argument?
Answer: D
The reasoning rests on a false premise. Sound and water waves need a material, but electromagnetic waves do not, so light crossing space fits both models. Choices A and B generalize from mechanical waves to all waves, and choice C denies the observation itself.
Question 9 of 20 · Multiple Choice
In the late 1880s, Heinrich Hertz made invisible electromagnetic waves with electric sparks and showed that they reflect, refract and form standing waves, traveling at about the speed of light. How did this evidence affect the model of light?
Answer: B
Maxwell's theory predicted electromagnetic waves traveling at the speed of light; Hertz's waves showed wave behavior (standing waves) at that speed, so light fit the same family. Choice C misses that visible light and radio waves differ only in frequency. Choice A reverses the evidence, and choice D is impossible: Hertz's own work was the first to notice the photoelectric effect.
Question 10 of 20 · Multiple Choice
After the photoelectric effect was explained with packets of energy, what happened to the wave model of light?
Answer: C
New evidence modified the theory rather than erasing the old evidence: fringes and radio antennas still need the wave model, and absorption of light by electrons needs packets. Choice A ignores all the wave evidence. Choices B and D are not supported by any evidence in this lesson.
Question 11 of 20 · Multiple Choice
Invented photoelectric data for a metal lie on a straight line through (8.0 × 10¹⁴ Hz, 0.50 V) and (10.0 × 10¹⁴ Hz, 1.30 V). What is the threshold frequency?
Answer: A
The slope is (1.30 - 0.50) ÷ 2.0 = 0.40 V per 10¹⁴ Hz. The voltage reaches zero 0.50 ÷ 0.40 = 1.25 × 10¹⁴ Hz below 8.0, at 6.75 × 10¹⁴ Hz. Choice B is the first data point, where electrons already leave. Choice C forgets to divide the 0.80 V rise by the 2.0 × 10¹⁴ Hz step, so it uses a slope of 0.80 V per 10¹⁴ Hz and puts the zero only 0.50 ÷ 0.80 ≈ 0.6 × 10¹⁴ Hz below 8.0. Choice D subtracts 0.50 from 8.0, mixing volts with frequency units.
Question 12 of 20 · Multiple Choice
For which task is the particle model of light more useful?
Answer: D
Separate clicks show light being absorbed in whole packets, one at a time. Choices A and C are interference and diffraction, and choice B is resonance, which the wave model handles directly.
Question 13 of 20 · Multiple Choice
A metal needs 3.2 × 10⁻¹⁹ J to free an electron. Light of intensity 2.0 × 10⁻³ W/m² shines on it. If, as in the wave model, each atom collects energy over an area of 1.0 × 10⁻¹⁹ m², how long would an electron have to wait?
Answer: C
Power per atom = (2.0 × 10⁻³ W/m²)(1.0 × 10⁻¹⁹ m²) = 2.0 × 10⁻²² W, so t = 3.2 × 10⁻¹⁹ J ÷ 2.0 × 10⁻²² W = 1,600 s, about 27 minutes. Choice A divides power by energy. Choice B drops the 10⁻³ from the intensity, as if it were 2.0 W/m². Choice D divides the energy by the intensity alone and leaves out the collecting area. The observed delay is essentially zero, which is evidence against the wave model for absorption.
Question 14 of 20 · Multiple Choice
A two-slit experiment is repeated with light so faint that a detector screen records one flash at a time. Each flash lands at one spot, but after many thousands of flashes the familiar bright and dark fringes appear. Which conclusion do these observations best support?
Answer: A
Single flashes show absorption in packets, and the pattern they build up matches the wave prediction. Choice B is ruled out because the same fringes appear at any brightness. Choice C cannot be right because the flashes arrive one at a time and cannot collide. Choice D ignores that each model explains part of the evidence.
Question 15 of 20 · Short Answer
Evaluate this argument, judging the claim, evidence and reasoning separately: "Claim: light is a stream of particles. Evidence: when a lamp of one color is made brighter, a metal plate gives off more electrons each second. Reasoning: a brighter lamp sends more particles, and more particles knock out more electrons."
Evidence: accurate (the photoelectric current grows with brightness), but it fits both models: in the wave model a brighter wave delivers more energy each second, so it also predicts more electrons. Reasoning: consistent with the particle model but incomplete, because it never shows that the wave model fails; evidence that both models explain cannot decide between them. Claim: not established by this evidence. A stronger argument would use what the wave model cannot explain: the fastest electrons have the same energy at every brightness, and light below a threshold frequency frees no electrons however bright it is.
Question 16 of 20 · Short Answer
Blue light (450 nm) passes through a single slit 0.090 mm wide onto a screen 1.80 m away. The wave model predicts a central bright band of width 2λL/a. Find the width, and explain what would happen to the band if the slit were made narrower.
Width = 2(450 × 10⁻⁹ m)(1.80 m) ÷ (0.090 × 10⁻³ m) = 0.018 m = 18 mm. A narrower slit makes the band wider, because the spreading grows as the opening gets smaller compared with the wavelength. A straight-line particle model would predict the opposite, a narrower strip.
Question 17 of 20 · Short Answer
Use the sodium line in Diagram 2 (0.414 V per 10¹⁴ Hz, threshold about 5.51 × 10¹⁴ Hz) to predict the stopping voltage for light of 9.5 × 10¹⁴ Hz. Then predict what a very bright lamp at 5.2 × 10¹⁴ Hz would do, and name the model that makes each prediction.
Stopping voltage = 0.414 × (9.5 - 5.51) ≈ 1.65 V. The lamp at 5.2 × 10¹⁴ Hz is below the threshold, so it ejects no electrons at any brightness. Both predictions come from the particle model and the data pattern; the wave model would predict electrons at any frequency after a delay, with more energy from a brighter lamp.
Question 18 of 20 · Short Answer
A 2.4 GHz Wi-Fi router uses antennas about a quarter of a wavelength long. Find the wavelength and the antenna length, and explain which model of electromagnetic radiation the design relies on.
λ = c ÷ f = 3.00 × 10⁸ ÷ 2.4 × 10⁹ = 0.125 m = 12.5 cm, so a quarter wavelength is about 3.1 cm. The design relies on the wave model: the antenna resonates with the oscillating field when its length fits the wavelength, just as a microwave oven cavity has hot spots half a wavelength apart.
Question 19 of 20 · Short Answer
Describe how the scientific model of light changed from 1704 to 1916. Name one piece of evidence that caused each change.
Model answer: Newton (1704) described light as particles, which explained straight-line travel and, he argued, refraction. Young's two-slit fringes (early 1800s) supported a wave model, and Foucault's 1850 measurement that light is slower in water ruled out Newton's prediction. Maxwell's theory and Hertz's radio waves (1887) made the electromagnetic wave model very strong. The photoelectric effect (Lenard's 1902 finding that electron energy depends on frequency, not brightness) could not be explained by waves; Einstein proposed energy packets in 1905, and Millikan's measurements (1916) confirmed the prediction. The result was not a return to Newton but a model in which light shows wave behavior and particle behavior, each more useful in different situations.
Question 20 of 20 · Short Answer
Choose the more useful model for each situation and justify it with evidence: (a) the colors of a soap bubble; (b) why ultraviolet light from the Sun can trigger a chemical change in a photochromic lens that bright indoor light does not; (c) why a car radio can still receive an AM station from behind a large building, where there is no straight line to the transmitter.
(a) Wave: light reflected from the front and back of the thin film interferes, and the thickness decides which colors add. (b) Particle: each UV packet carries enough energy to trigger the change in one molecule, while visible packets do not, however many arrive. (c) Wave: AM radio waves are hundreds of meters long, comparable to the size of the building, so they diffract around it; particles moving in straight lines would leave a sharp shadow behind it.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does HS-PS4-3 mean?
HS-PS4-3 asks students to evaluate the claims, evidence and reasoning for describing electromagnetic radiation as a wave or as particles, and to recognize that one model is more useful than the other in some situations. The code means High School, Physical Science, core idea 4 (Waves and Their Applications in Technologies for Information Transfer), performance expectation 3.
Is HS-PS4-3 taught in physics or chemistry?
It is usually taught in Physics, in a unit on waves and electromagnetic radiation after HS-PS4-1. Chemistry courses touch the same ideas when they discuss light and electrons in atoms, but the evidence-and-argument focus of this standard fits a physics or physical science course best.
What is the assessment boundary for HS-PS4-3?
The official Assessment Boundary says: "Assessment does not include using quantum theory." Students argue from evidence about the two models, but they are not assessed on quantum mechanics. Many teachers read this as leaving out calculations of photon energy with Planck's constant, as this lesson does, and keeping the math to wave relations and energy = power × time.
Is light a wave or a particle?
Neither model alone describes all of its behavior. Light spreads, interferes and resonates like a wave, and it is absorbed and emitted in separate packets of energy like particles. Physicists use the model that fits the situation: the wave model for how light travels and combines, the particle model for how it delivers energy to single electrons or molecules.
What evidence supports the wave model of light?
The clearest evidence is interference: two beams of light can cancel each other and make dark fringes, which particles moving in straight lines cannot do. Diffraction (light spreading after a narrow opening), resonance of microwaves in a cavity and the measured speed of light in water add to the case. The evidence examples on this page work through each one.
What is the photoelectric effect in simple terms?
It is light knocking electrons out of a metal surface. Measurements showed three surprises for the wave model: a threshold frequency, a lack of delay in dim light and electron energies set by the color of the light rather than its brightness. These results led Einstein to propose in 1905 that light energy arrives in packets.
Why did scientists keep the wave model after the photoelectric effect?
Because the old evidence did not go away. Interference, diffraction and radio waves are still explained by waves, so the theory was modified to include both kinds of behavior instead of being replaced. This is a good example of the Clarification Statement's emphasis on how a theory changes in light of new evidence.
Can the HS-PS4-3 labs be done safely in a high school classroom?
Yes, with care. Use class 2 laser pointers (under 1 mW) and never point them at anyone. The microwave-oven chocolate test should be run by the teacher with no metal inside. UV flashlights need UV-blocking glasses and should never be looked into. The photoelectric effect itself is best shown by video or simulation, since the lamps that produce it for zinc give off strong ultraviolet light.
Do students need math for HS-PS4-3?
Some, but the math serves the argument. Students use c = fλ, the fringe spacing λL/d and energy = power × time to test predictions, and they read a threshold from a graph. Calculations of photon energy with Planck's constant are beyond this standard.
How does HS-PS4-3 connect to other standards?
It builds on MS-PS4-2 (how waves interact with materials) and HS-PS4-1 (the frequency-wavelength-speed relationship). It pairs with HS-PS4-4, which evaluates claims about the effects of different frequencies of radiation absorbed by matter, and with RST.11-12.8 on evaluating evidence in scientific texts. HS-PS4-5 applies both models to devices such as solar cells and fiber optics.
07
Related Standards
5 standards
These standards connect to HS-PS4-3: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
MS-PS4-2Prerequisite
Model how waves are reflected, absorbed or transmitted through various materials
NGSS is a registered trademark of WestEd. Neither WestEd nor the lead states and partners that developed the Next Generation Science Standards were involved in the production of this product, and do not endorse it.
