Experimental study of the photoelectric effect
Photocurrent grows with intensity. The stopping potential grows with frequency but does not depend on intensity, and there is no emission below the threshold frequency.
The apparatus and method
An evacuated glass or quartz tube holds a photosensitive plate C (the emitter) and another metal plate A (the collector).
- 1Monochromatic light enters through a quartz window and falls on C. Quartz lets ultraviolet light through, but ordinary glass does not.
- 2A battery keeps a potential difference between C and A. A potential divider changes it, and a commutator reverses its direction.
- 3A voltmeter reads the potential of A with respect to C, and a microammeter reads the photocurrent.
- 4Electrons emitted from C travel to A, so a current flows in the outer circuit.
- 5Change one thing at a time, the intensity, the potential of A or the frequency, and record the current.
What the experiment shows
| Change made | Observation | Shape of graph |
|---|---|---|
| Intensity increased (frequency and potential fixed) | Photocurrent increases in direct proportion | Straight line through the origin |
| A made more and more positive | Current rises, then stays at a maximum: the saturation current | Curve rising to a flat top |
| A made negative (retarding potential) | Current falls and becomes zero at the stopping potential −V₀ | Curve meeting the voltage axis at −V₀ |
| Different intensities, same frequency | Higher intensity gives a larger saturation current, but the same V₀ | Curves start from the same point −V₀ |
| Different frequencies, same intensity | The same saturation current, but V₀ is larger for higher frequency | Curves start from different points |
| V₀ plotted against frequency ν | Straight line; V₀ = 0 at the threshold frequency ν₀ | Line cutting the ν axis at ν₀ |
Laws of photoelectric emission
- For a given metal and frequency, the photocurrent is directly proportional to the intensity of light.
- The saturation current is proportional to intensity, but the stopping potential does not depend on intensity.
- Above the threshold frequency, the stopping potential (and so K_max) increases linearly with frequency.
- Below the threshold frequency ν₀, no emission takes place, however intense the light.
- Emission is instantaneous: the time lag is about 10⁻⁹ s or less, even with very dim light.
How to draw the apparatus
- Draw an evacuated tube (an oval). Inside, draw plate C (emitter) on the left and plate A (collector) on the right.
- Draw a quartz window on the tube and wavy arrows of light falling on C.
- Outside, join C and A through a battery with a potential divider and a commutator (reversing key).
- Put a microammeter (μA) in series in the circuit, and a voltmeter (V) across C and A.
- Mark the path of electrons from C to A with small arrows labelled e⁻.
How to draw the photoelectric graphs
- Current vs intensity: a straight line from the origin. Label the axes photocurrent and intensity.
- Current vs collector potential, two intensities (I₂ > I₁): both curves start from the same point −V₀ on the negative voltage axis, rise, and level off. The I₂ curve levels off higher.
- Current vs collector potential, three frequencies (ν₃ > ν₂ > ν₁): the curves start at −V₀₃, −V₀₂ and −V₀₁, with ν₃ farthest left, and all level off at the same saturation current.
- V₀ vs ν: a straight line starting at ν₀ on the frequency axis. For a second metal, draw a parallel line starting at a different ν₀.
Worked example: from stopping potential to speed
In a photocell, the photocurrent becomes zero when the collector is at −1.5 V with respect to the emitter. Find the maximum kinetic energy of the photoelectrons in eV and in joules, and their maximum speed. (mₑ = 9.11 × 10⁻³¹ kg, e = 1.6 × 10⁻¹⁹ C)
- At the stopping potential, eV₀ = K_max.
- K_max = e × 1.5 V = 1.5 eV.
- In joules: 1.5 × 1.6 × 10⁻¹⁹ J = 2.4 × 10⁻¹⁹ J.
- ½mv² = K_max, so v = √(2K_max/m) = √(2 × 2.4 × 10⁻¹⁹ ÷ 9.11 × 10⁻³¹) m/s.
- v = √(5.27 × 10¹¹) m/s ≈ 7.3 × 10⁵ m/s.
K_max = 1.5 eV = 2.4 × 10⁻¹⁹ J; maximum speed ≈ 7.3 × 10⁵ m/s
Some sensors switch street lights on at dusk. Their current grows with the intensity of light, just as the photocurrent does in this experiment.
3 marks: “Draw graphs showing how photocurrent varies with collector plate potential for (a) two intensities at the same frequency, (b) two frequencies at the same intensity. What does each graph show?” (a) Same −V₀, different saturation currents: V₀ does not depend on intensity. (b) Different −V₀, same saturation current: V₀ increases with frequency.
2 marks: “Define stopping potential. How is it related to the maximum kinetic energy of the photoelectrons?” The smallest negative potential of the collector at which the photocurrent becomes zero. eV₀ = K_max = ½mv²max.
5 marks: “Describe an experiment to study the photoelectric effect with a labelled diagram, and state the laws of photoelectric emission.” Evacuated tube with emitter C and collector A, quartz window, battery with potential divider and commutator, voltmeter, microammeter; vary intensity, potential and frequency; laws: current ∝ intensity, V₀ independent of intensity, V₀ linear in ν, threshold ν₀, no time lag; graphs.
Intensity decides how many; frequency decides how fast. Saturation current follows intensity; stopping potential follows frequency.