7.2 - Photoelectric Effect

Photoelectric Effect and the Photocell Circuit

• Photoelectric effect is the emission of electrons from a metal surface illuminated by light of a suitable frequency. The emitted electrons are photoelectrons.
• In the photocell circuit:
  1. Light illuminates the light-sensitive metal cathode, releasing photoelectrons.
  2. The anode at positive potential attracts the photoelectrons through the vacuum.
  3. Their movement from cathode to anode produces current in the circuit, measured by a milliammeter. A battery supplies the potential difference.

Determining Planck’s Constant with LEDs

• Aim: determine Planck’s constant using a Planck’s constant kit.
• Apparatus: a 9 V battery, 1 kΩ potentiometer, red, orange, green and blue LEDs, milliammeter and voltmeter.
• Procedure and analysis:
  1. Connect the kit using the red LED, with the milliammeter measuring LED current and the voltmeter measuring the voltage across the LED.
  2. Adjust the potentiometer to 0.2 V and record the current.
  3. Repeat at 0.4 V, 0.6 V, 0.8 V, …, 3.0 V.
  4. Plot current $I$ against voltage $V$. Determine the activation voltage $V_a$ from the voltage-axis intercept.
  5. Repeat with orange, green and blue LEDs.
  6. Record $V_a$ and calculate $1/\lambda$ for each LED, expressing wavelength in metres.
  7. Plot $V_a$ against $1/\lambda$, determine the gradient $m$ and calculate $h$.

LED colour	Wavelength / nm
Red	623
Orange	586
Green	567
Blue	467

• $e=1.60\times 10^{-19}\mathrm{C}$ and $c=3.00\times 10^8{\mathrm{m}\mathrm{s}}^{-1}$.
• Relationship: $V_a$ has a linear relationship with $1/\lambda$; shorter LED wavelength corresponds to higher activation voltage.

Four Characteristics of the Photoelectric Effect

1. Higher frequency produces photoelectrons with higher kinetic energy.
2. A metal has a threshold frequency $f_0$, the minimum light frequency required for photoelectric emission.
3. Kinetic energy is independent of light intensity. Increasing intensity does not make photoelectrons more energetic.
4. Emission is instantaneous when suitable-frequency light strikes the surface, even at low intensity. Thermionic emission requires heating and may take time.

Why Classical Theory Fails

Classical prediction	Experimental observation
Continuous wave energy should permit emission at any light frequency.	Emission requires a minimum frequency; increasing intensity cannot remove this requirement.
Dim light should require time for electrons to accumulate sufficient energy.	Suitable-frequency light produces instantaneous emission even when dim.