Photoelectric effect: the experiment, stopping potential and graphs
Photocurrent grows with intensity, but the stopping potential grows only with frequency. Below the threshold frequency no electrons come out, however bright the light.
The apparatus and method
A metal cup C, the **photocathode**, and a collector plate A are sealed in an evacuated glass tube.
- 1Light of one frequency enters through a quartz window and falls on C. Quartz lets ultraviolet light through; ordinary glass does not.
- 2A battery keeps a potential difference between A and C. A commutator (reversing key) can make A positive or negative with respect to C.
- 3A microammeter (μA) reads the photocurrent, the current carried by the emitted electrons.
- 4★Change one thing at a time: the intensity of light, the potential of A, or the frequency, and record the current.
★ key step
Plate positive, then plate negative
When A is positive, it pulls the emitted electrons. Raising its voltage increases the current, until every emitted electron is collected. The current then stays constant: the saturation current. The plate voltage at which this first happens is the saturating voltage. When A is negative, it pushes the electrons back. Only the fastest ones still reach A. As the negative voltage grows, the current falls and at one value becomes zero. This is the stopping potential V₀. The work done against it equals the largest kinetic energy: eV₀ = ½mv²max.
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 |
| Plate A made more and more positive | Current rises, then stays at a maximum: the saturation current | Curve rising to a flat top |
| Plate 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 number of photoelectrons (and so the photocurrent) is proportional to the intensity of light.
- The maximum speed of photoelectrons does not depend on the intensity.
- The maximum speed increases with the frequency of light and depends on the metal used.
- For every metal there is a threshold frequency ν₀. Below it, no electrons come out, however bright the light.
- Emission is instantaneous: the time lag is only about 10⁻⁹ s, even with dim light.
How to draw the apparatus and the graphs
- Apparatus: an evacuated tube with photocathode C and plate A, a quartz window with light falling on C, a battery with a commutator, and a microammeter in series.
- Current against intensity: a straight line through the origin.
- Current against plate potential, two intensities (I₂ > I₁): both curves start from the same −V₀ and level off; the I₂ curve levels off higher.
- Current against plate potential, two frequencies (ν₁ > ν₂), same intensity: the ν₁ curve starts farther left (larger V₀); both reach the same saturation current.
- V₀ against ν: a straight line cutting the frequency axis at ν₀; write slope = h/e beside it.
Worked example: from stopping potential to speed
In a photoelectric experiment, the photocurrent becomes zero when plate A is at −1.5 V with respect to the photocathode. Find the maximum kinetic energy of the photoelectrons in eV and in joules, and their maximum speed. (m = 9.1 × 10⁻³¹ kg, e = 1.6 × 10⁻¹⁹ C)
- At the stopping potential, eV₀ = ½mv²max = 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.
- v = √(2K_max/m) = √(2 × 2.4 × 10⁻¹⁹ ÷ 9.1 × 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
Automatic street lights that switch on at dusk and the door sensors in shopping malls use the fact that photocurrent depends on how much light falls on a sensor.
2 marks: “Sketch the set-up used to study the photoelectric effect and label each part.” Evacuated tube with a quartz window; photocathode C and collector plate A; battery with a commutator to reverse the polarity; microammeter in series; light falling on C; electrons moving from C to A.
2 marks: “Draw graphs of photocurrent against plate potential for two intensities I₁ > I₂ of light of the same frequency. What do they show about the stopping potential?” Both curves start from the same −V₀ on the negative voltage axis; the I₁ curve saturates at a higher current. The stopping potential does not depend on intensity.
3 marks: “State the laws of photoelectric emission.” Photocurrent ∝ intensity; maximum kinetic energy does not depend on intensity; it rises with frequency; no emission below the threshold frequency ν₀; emission is instantaneous (about 10⁻⁹ s).
Brighter gives more, bluer gives faster: intensity sets the current, frequency sets the stopping potential.