The photoelectric effect experiment investigates the phenomenon in which electrons are emitted when light is incident on a metal surface.
Classical wave theory alone would predict that increasing the intensity of light should also increase the maximum kinetic energy of the electrons. In reality, however, the maximum kinetic energy of the emitted electrons is determined not by light intensity but by the frequency of the light.
This phenomenon shows that light behaves not only as a continuous wave but also as photons with energy hν. The photoelectric effect is an important experiment for understanding the foundations of quantum theory.
This article assumes an experiment in which light of different wavelengths is directed onto a photoelectric tube and the stopping voltage at which the photocurrent becomes zero is measured. It covers the introduction, precautions, items to record, sample experimental values, calculations, sources of error, an example results section, and example discussion.
Note:
This article is educational reference material for discussing results obtained in physics experiments at schools, universities, and similar institutions. The experimental conditions and measured values shown here are illustrative examples and are not actual experimental results.
Handle light sources, power supplies, photoelectric tubes, spectrometers, and other equipment according to your institution’s laboratory manual and the instructions of your instructor. Do not look directly at ultraviolet-containing or high-intensity light sources. When using equipment with a high-voltage power supply, do not touch terminals while power is on, and always switch off the power before changing wiring.
- What Is the Photoelectric Effect?
- Stopping Voltage
- Threshold Frequency and Cutoff Wavelength
- Effect of Light Intensity
- Main Items to Record in the Results
- Sample Experimental Conditions
- Sample Experimental Values
- Calculation Methods
- Main Sources of Error
- Example of How to Write the Results
- Points to Connect to the Discussion
- Discussion Example
- Summary
What Is the Photoelectric Effect?
The photoelectric effect is the phenomenon in which electrons are emitted from a metal when light with a frequency above a certain threshold is incident on its surface. The emitted electrons are called photoelectrons.
The energy of one photon is expressed as follows.
E = hν
Here, h is Planck’s constant and ν is the frequency of the light.
Part of the photon energy is used to overcome the work function φ, the energy required to remove an electron from the metal surface, and the remainder becomes the maximum kinetic energy of the photoelectron.
hν = φ + Kmax
This is known as Einstein’s photoelectric equation.
Stopping Voltage
When a voltage is applied opposite to the direction of photoelectron motion, the photocurrent gradually decreases. The voltage at which even photoelectrons with the maximum kinetic energy can no longer reach the anode and the photocurrent becomes zero is called the stopping voltage Vs.
Kmax = eVs
Therefore, the photoelectric equation can be written as follows.
eVs = hν − φ
Solving for the stopping voltage gives:
Vs = (h/e)ν − φ/e
If stopping voltage is plotted on the vertical axis and frequency on the horizontal axis, the ideal relationship is linear. Planck’s constant can be determined from the slope and the work function from the intercept.
Threshold Frequency and Cutoff Wavelength
The minimum frequency at which photoelectrons begin to be emitted is called the threshold frequency ν0.
hν0 = φ
Thus, the threshold frequency is:
ν0 = φ/h
The longest corresponding wavelength is called the cutoff wavelength λ0.
λ0 = c/ν0 = hc/φ
Effect of Light Intensity
If only the intensity is increased while the light frequency remains the same, the number of photons incident per unit time increases. Therefore, more photoelectrons are emitted and the photocurrent increases.
On the other hand, the energy of each photon is determined by frequency, so changing the light intensity ideally does not change the stopping voltage.
Main Items to Record in the Results
- Type of light source
- Wavelength of incident light
- Frequency of incident light
- Filter or spectrometer conditions
- Cathode material of the photoelectric tube
- Applied voltage
- Photocurrent
- Stopping voltage
- Light intensity
- Dark current
- Presence or absence of background light
- Graph of stopping voltage versus frequency
- Slope of the graph
- Intercept of the graph
- Planck’s constant
- Work function
- Threshold frequency
- Cutoff wavelength
- Relative error compared with the reference value
- Instrument resolution
Sample Experimental Conditions
| Item | Sample Condition |
|---|---|
| Light source | Mercury lamp or monochromatic LED |
| Photoelectric tube | Vacuum photoelectric tube |
| Cathode material | Alkali-metal photocathode |
| Wavelength range | 365–578 nm |
| Voltage measurement range | 0–2.5 V |
| Current measurement range | nA–µA |
| Voltmeter resolution | 0.01 V |
| Room temperature | 23 ℃ |
| Dark condition | Measured inside a light-shielding box |
Sample Experimental Values
Wavelength, Frequency, and Stopping Voltage
| Wavelength λ (nm) | Frequency ν (1014 Hz) | Stopping Voltage Vs (V) |
|---|---|---|
| 578 | 5.19 | 0.30 |
| 546 | 5.49 | 0.43 |
| 436 | 6.88 | 1.01 |
| 405 | 7.40 | 1.23 |
| 365 | 8.22 | 1.57 |
Changing Light Intensity at the Same Wavelength
The following illustrative data use light with a wavelength of 436 nm.
| Relative Light Intensity (%) | Saturation Photocurrent (nA) | Stopping Voltage (V) |
|---|---|---|
| 25 | 18 | 1.00 |
| 50 | 36 | 1.01 |
| 75 | 54 | 1.00 |
| 100 | 72 | 1.01 |
Example of Applied Voltage and Photocurrent
The following illustrative data are for a wavelength of 436 nm at constant light intensity.
| Applied Voltage (V) | Photocurrent (nA) |
|---|---|
| +2.0 | 71 |
| +1.0 | 68 |
| 0.0 | 49 |
| −0.4 | 31 |
| −0.8 | 12 |
| −1.0 | 1 |
| −1.1 | 0 |
Calculation Methods
Converting Wavelength to Frequency
Let the speed of light be c = 3.00 × 108 m/s and the wavelength be 436 nm.
ν = c/λ
= (3.00 × 108)/(436 × 10−9)
= 6.88 × 1014 Hz
Maximum Kinetic Energy
For a stopping voltage of 1.01 V, the maximum kinetic energy of a photoelectron is:
Kmax = eVs
= (1.602 × 10−19) × 1.01
= 1.62 × 10−19 J
In electron volts, a stopping voltage of 1.01 V corresponds to a maximum kinetic energy of 1.01 eV.
Determining Planck’s Constant from the Graph Slope
Suppose the slope of the stopping-voltage-versus-frequency graph is 4.14 × 10−15 V·s.
Slope a = h/e
h = ea
= (1.602 × 10−19) × (4.14 × 10−15)
= 6.63 × 10−34 J·s
Determining the Work Function from the Intercept
If the vertical-axis intercept is −1.85 V, the stopping-voltage equation shows that the intercept equals −φ/e.
φ/e = 1.85 V
Therefore, the work function is 1.85 eV. Converting to joules gives:
φ = 1.85 × 1.602 × 10−19
= 2.96 × 10−19 J
Threshold Frequency
ν0 = φ/h
= (2.96 × 10−19)/(6.63 × 10−34)
= 4.46 × 1014 Hz
Cutoff Wavelength
λ0 = c/ν0
= (3.00 × 108)/(4.46 × 1014)
= 6.73 × 10−7 m
= 673 nm
Relative Error of Planck’s Constant
For an experimental value of 6.63 × 10−34 J·s and a reference value of 6.626 × 10−34 J·s:
Relative error (%) = |experimental value − reference value|/reference value × 100
= |6.63 − 6.626|/6.626 × 100
= 0.06%
Main Sources of Error
| Source of Error | Effect on Measurement | Likely Tendency in Results | Improvement |
|---|---|---|---|
| Determination of stopping voltage | It is difficult to identify the exact point where photocurrent becomes zero | Stopping voltage varies between readings | Create an I-V curve and extrapolate |
| Dark current | A small current flows even without illumination | Photocurrent does not reach zero, tending to make the stopping voltage appear larger | Measure and subtract the dark current |
| Background light | Unwanted light reaches the photocathode | Additional photocurrent is generated | Use a light-shielding box |
| Insufficient monochromatic purity | Multiple wavelengths are incident simultaneously | Short-wavelength components can increase the stopping voltage | Use an appropriate filter or spectrometer |
| Wavelength reading error | Frequency conversion is shifted | The graph slope changes | Calibrate the wavelength |
| Voltmeter zero offset | A constant bias is added to all stopping voltages | Mainly shifts the intercept and work function | Check zero before measurement |
| Contact potential difference | An inherent potential difference exists between electrode materials or connections | A constant offset is added to stopping voltage | Correct it as an apparatus constant |
| Contamination or oxidation of photocathode | The work function changes | Threshold frequency and stopping voltage change | Store the photoelectric tube properly |
| Light-source intensity fluctuations | Photocurrent changes over time | The I-V curve becomes unstable | Allow the light source to stabilize sufficiently |
| Space-charge effect | Repulsion between emitted electrons hinders electron motion | Photocurrent becomes less proportional at high light intensity | Measure at an appropriate light intensity |
| Electrode geometry and nonuniform electric field | Electron collection efficiency varies with position | The I-V curve deviates from the ideal shape | Keep apparatus geometry constant |
| Internal resistance of measuring instruments | Circuit conditions deviate from the ideal | Small-current readings change | Use a high-input-resistance voltmeter |
| Narrow frequency range | The slope is difficult to determine accurately | Uncertainty in Planck’s constant increases | Measure multiple points over a broad wavelength range |
| Too few points for linear regression | An error in one point strongly affects the slope | Planck’s constant becomes unstable | Increase the number of measurement points |
Why Stopping Voltage Increases with Light Frequency
The energy of one photon is hν, and the portion exceeding the work function becomes the maximum kinetic energy of the photoelectron. Therefore, a higher frequency gives photoelectrons greater maximum kinetic energy, requiring a larger stopping voltage to stop them.
Why Increasing Light Intensity Does Not Change Stopping Voltage
Increasing light intensity increases the number of photons incident per unit time. Therefore, the number of emitted electrons and the photocurrent increase.
However, the energy per photon is determined by frequency. At the same frequency, the maximum kinetic energy of each photoelectron does not change, so the stopping voltage remains approximately constant.
Why Light Below the Threshold Frequency Does Not Emit Electrons
For light below the threshold frequency, the energy hν of one photon is smaller than the work function φ. Therefore, even if the light intensity is increased and the number of photons rises, a single photon does not have enough energy to remove an electron from the metal surface.
Why the Photoelectric Effect Demonstrates the Particle Nature of Light
The facts that the maximum kinetic energy of electrons is determined by light frequency rather than intensity, and that a threshold frequency exists, can be explained by treating light energy as being delivered in discrete photon units rather than continuously.
Example of How to Write the Results
Monochromatic light with wavelengths from 578 to 365 nm was directed onto a photoelectric tube, and the stopping voltage was measured for each wavelength.
The stopping voltage increased as the wavelength became shorter and the frequency became higher. A graph of stopping voltage versus frequency was approximately linear.
The slope of the regression line was 4.14 × 10−15 V·s, from which Planck’s constant was determined to be 6.63 × 10−34 J·s.
From the vertical-axis intercept, the work function of the photocathode was determined to be 1.85 eV, the threshold frequency 4.46 × 1014 Hz, and the cutoff wavelength 673 nm.
Points to Connect to the Discussion
- Was the relationship between stopping voltage and frequency linear?
- Was Planck’s constant obtained from the graph slope close to the reference value?
- Was the work function obtained from the vertical-axis intercept reasonable?
- Were the threshold frequency and cutoff wavelength consistent with the properties of the photocathode?
- When light intensity was changed at the same frequency, did the photocurrent change?
- Did the stopping voltage remain approximately constant when light intensity was changed?
- Was dark current corrected?
- Was background light sufficiently blocked?
- Was the incident light sufficiently monochromatic?
- How was the stopping voltage determined?
- Was there any effect from contact potential difference?
- Were the number of measurement points and the frequency range sufficient?
- How were outliers in the regression handled?
Discussion Example
In this experiment, light of different wavelengths was directed onto a photoelectric tube, and the relationship between light frequency and the maximum kinetic energy of photoelectrons was investigated by measuring the stopping voltage at which the photocurrent became zero.
The results showed that the stopping voltage increased as the wavelength became shorter and the frequency became higher. This is because the energy of one photon is given by hν, so increasing the frequency increases the energy transferred to a photoelectron.
The graph of stopping voltage versus frequency was approximately linear, showing a trend consistent with Einstein’s photoelectric equation eVs = hν − φ.
The slope of the regression line was 4.14 × 10−15 V·s. Using the electron charge, Planck’s constant was calculated to be 6.63 × 10−34 J·s. This value is close to the reference value of 6.626 × 10−34 J·s, confirming that Planck’s constant can be determined from the photoelectric effect.
The work function obtained from the vertical-axis intercept was 1.85 eV. The work function is the minimum energy required to remove an electron from the photocathode and varies with the material and surface condition.
When the light intensity was changed at the same wavelength, the saturation photocurrent increased approximately in proportion to light intensity. In contrast, the stopping voltage remained almost constant at about 1.00–1.01 V.
This can be explained by the increase in the number of photons incident per unit time as light intensity increases, which increases the number of emitted photoelectrons and therefore the photocurrent.
However, because the energy of each photon is determined by light frequency, the maximum kinetic energy of each photoelectron does not change at the same frequency, so the stopping voltage also remains unchanged.
This result indicates that light energy is transferred to electrons in photon units rather than being distributed continuously, supporting the particle nature of light.
One source of error is the determination of stopping voltage. In actual measurements, a small current may remain near the stopping voltage because of dark current, background light, and instrument noise, making it difficult to directly identify the exact point at which photocurrent becomes zero.
To determine the stopping voltage more accurately, it is effective to measure current and voltage at several points near the stopping voltage and extrapolate a line or suitable curve to the voltage at zero current.
If dark current is not subtracted when determining the stopping voltage, current that flows even without illumination is treated as photocurrent, potentially causing the stopping voltage to be measured too high.
If the incident light is not perfectly monochromatic and contains components with wavelengths shorter than the intended wavelength, those components can emit electrons with greater kinetic energy, potentially increasing the measured stopping voltage.
Contact potential differences between electrodes and voltmeter zero offsets introduce an approximately constant shift into all stopping-voltage measurements. This mainly affects the graph intercept rather than the slope, and therefore can have a large effect on the measured work function.
In contrast, wavelength calibration errors change the frequency values on the horizontal axis and therefore affect both the regression slope and the resulting value of Planck’s constant.
Measurement accuracy can be improved by sufficiently blocking external light, measuring and correcting dark current under each condition, using wavelength-calibrated monochromatic light, increasing the number of measurements near the stopping voltage, and performing regression over a broad frequency range.
In conclusion, the stopping voltage was approximately proportional to the frequency of light and remained nearly constant when light intensity was changed. These results are consistent with the photon-energy relation hν and confirm that the photoelectric effect demonstrates the particle nature of light.
Discussion Example When Planck’s Constant Is Larger Than the Reference Value
Possible reasons for obtaining a Planck constant larger than the reference value include reading the stopping voltage too high on the high-frequency side, contamination by shorter-wavelength components, or overestimating the wavelength and therefore calculating a frequency that is too low.
Discussion Example When Planck’s Constant Is Smaller Than the Reference Value
Possible reasons for obtaining a Planck constant smaller than the reference value include reading the stopping voltage too low on the high-frequency side, underestimating the wavelength, or using different criteria for determining the stopping voltage at different wavelengths.
Discussion Example When the Graph Is Not Linear
Possible reasons why the stopping-voltage-versus-frequency graph was not linear include differences in monochromatic purity among wavelengths, insufficient correction for dark current or background light, variation in determining the stopping voltage, or changes in photocathode sensitivity during measurement.
Discussion Example When Stopping Voltage Appears to Change with Light Intensity
If the stopping voltage appeared to change with light intensity, possible causes include a change in the wavelength distribution when the intensity was adjusted, a space-charge effect under strong illumination, or different criteria for judging the small current near the stopping voltage at different intensities.
Summary
In the photoelectric effect, the portion of the photon energy hν that exceeds the work function becomes the maximum kinetic energy of the photoelectron.
The relationship between stopping voltage and light frequency is linear, allowing Planck’s constant to be determined from the slope and the work function from the intercept.
Increasing light intensity at the same frequency increases the photocurrent, but ideally does not change the stopping voltage.
In the discussion, it is important to relate dark current, background light, monochromatic purity, determination of stopping voltage, contact potential difference, and wavelength calibration to how the measured Planck constant and work function differ from reference values.
