7.2 Photoelectric Effect
When a metal surface is illuminated by a beam of light at a certain frequency, electrons can be emitted from the metal surface. This phenomenon is known as the photoelectric effect, and the emitted electrons are called photoelectrons.
Learning Objectives
- State the definition of the photoelectric effect and photoelectrons.
- Describe the operation of a photocell circuit to detect photoelectric current.
- Determine the value of Planck's constant, \(h\), using a Planck's constant kit and graphical analysis (\(V_a\) against \(\frac{1}{\lambda}\)).
- State and explain the four key characteristics of the photoelectric effect obtained experimentally.
- Define threshold frequency (\(f_0\)).
- Compare the classical wave theory predictions with experimental results regarding frequency, intensity, and emission time.
Apparatus to Demonstrate the Photoelectric Effect
See how photons eject photoelectrons from the cathode to produce a measurable current at the anode.
Photocell Circuit
How It Works
1. Light strikes the light-sensitive cathode.
2. Photoelectrons are emitted from the metal surface.
3. The positive anode attracts the photoelectrons.
4. The moving electrons create a current detected by the milliammeter.
Short Explanation
What is the Photoelectric Effect?
The photoelectric effect is the phenomenon where electrons are emitted from a metal surface when it is illuminated by a beam of light at a certain frequency. The emitted electrons are called photoelectrons.
Threshold Frequency
The minimum frequency of light needed for a metal to emit electrons is known as the threshold frequency, \(f_0\), for that metal.
Determining Planck's constant, \(h\)
\(h = \dfrac{me}{c}\)where \(m\) is the gradient of the graph of \(V_a\) against \(\frac{1}{\lambda}\), \(e = 1.60 \times 10^{-19}\ \mathrm{C}\) is the charge of an electron, and \(c = 3.00 \times 10^8\ \mathrm{m\,s^{-1}}\) is the speed of light in vacuum.
| Characteristic | Experimental Observation |
|---|---|
| Effect of frequency on kinetic energy | The higher the frequency of the photon of light, the higher the kinetic energy of the photoelectrons emitted from the metal surface. |
| Threshold frequency | Emission only occurs when light frequency exceeds the threshold frequency, \(f > f_0\). |
| Effect of light intensity | The kinetic energy of photoelectrons does not depend on the intensity of light. Higher intensity emits more photoelectrons, but does not increase their kinetic energy. |
| Instantaneous emission | Photoelectrons are emitted instantaneously when a metal surface is illuminated by light, provided frequency exceeds the threshold frequency. |
| Classical Wave Theory | Experimental Findings |
|---|---|
| Light is a continuous wave. Emission should occur at any frequency. | Photoelectron emission only occurs when light frequency exceeds a threshold frequency, \(f > f_0\), regardless of intensity. |
| Bright light should emit electrons quickly; dim light should emit electrons after a time lag. | Photoelectron emission is instantaneous even at low light intensities. |
Try to Answer First
Answer in your mind, then press “Check Answer”.
What is meant by the threshold frequency, \(f_0\)?
Check Answer
Does increasing the intensity of light increase the kinetic energy of the photoelectrons? Explain.
Check Answer
How can Planck's constant, \(h\), be determined from the gradient, \(m\), of a graph of activation voltage \(V_a\) against \(\frac{1}{\lambda}\)?
Check Answer
Common Mistakes
- Confusing light intensity with light frequency: assuming brighter light ejects faster (higher kinetic energy) electrons.
- Assuming dim light takes longer to emit electrons, following classical wave theory rather than experimental quantum observations.
- Confusing threshold frequency (\(f_0\)) with the activation voltage (\(V_a\)) of an LED.
- Plotting \(V_a\) against \(\lambda\) instead of \(\frac{1}{\lambda}\), which results in an inverse curve instead of a straight-line graph.
Concept Misunderstandings
Light of any frequency will eventually cause photoelectric emission if the light is bright enough or left shining for a long time.
If the incident light frequency is below the threshold frequency (\(f < f_0\)), photoelectric emission will never occur, no matter how bright the light is or how long it illuminates the surface.
Increasing light intensity increases the kinetic energy of emitted photoelectrons.
Light intensity only affects the number of photons striking the surface per second, while the frequency determines the energy of each photon and the resulting kinetic energy of the photoelectrons.
Summary
- Photoelectric effect is the ejection of electrons (photoelectrons) from a metal surface when illuminated by light of sufficient frequency.
- In a photocell, photoelectrons emitted from the cathode travel to the anode, generating a measurable electric current.
- Planck's constant \(h\) can be calculated from the gradient \(m\) of a \(V_a\) versus \(\frac{1}{\lambda}\) graph using \(h = \dfrac{me}{c}\).
- Kinetic energy of photoelectrons increases with photon frequency.
- Emission requires incident frequency to be at or above threshold frequency (\(f \ge f_0\)).
- Kinetic energy is independent of light intensity.
- Emission of photoelectrons is instantaneous upon illumination.
Short Activity
Objective: Test your understanding of the photoelectric effect, threshold frequency and Planck's constant.
A. Objective Quiz
1 Which characteristic of incident light determines the kinetic energy of the emitted photoelectrons?
2 What happens when a metal surface is illuminated by light with a frequency lower than its threshold frequency, \(f_0\)?
B. Fill in the Blanks
3 The minimum frequency of light required to emit photoelectrons from a metal surface is called the frequency.
4 In an experiment plotting activation voltage \(V_a\) against \(\frac{1}{\lambda}\), the gradient \(m\) of the graph equals .
C. Matching / Drag and Drop
Drag each term to the correct description. If using a phone, tap the answer first, then tap the matching box.
