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4.11.3Electrons, Waves and Photons

Determining the Planck Constant — OCR A Level Physics A H556 Revision Notes & Topical Questions

5 min read 6 parts Lesson 20 of 62 Unit quiz

📚 OCR A Level Physics A H556 Hub / Topical Revision
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Part 1 of 6The Principle

4.11.3 Determining the Planck Constant
LED turn-on
  • An LED just begins to emit light when the potential difference across it supplies each electron with enough energy to produce one photon.
Energy equation
  • At the threshold, the electron energy eV equals the photon energy hc/λ, so V = (hc/e) × (1/λ).
Straight line
  • A graph of threshold voltage V against 1/λ is a straight line through the origin, with gradient hc/e.
Finding h
  • The Planck constant follows from h = (gradient × e) / c.

Part 2 of 6Method

1
Use several LEDs of different colours with known wavelengths, each in series with a protective resistor.
2
Connect a voltmeter across the LED and use a variable supply or potential divider to increase the voltage slowly.
3
Shield the LED from room light, for example with a dark tube, and watch for the first faint glow.
4
Record the voltage at which the LED just lights, then repeat several times and take a mean for each colour.
5
Calculate 1/λ for each LED and plot V against 1/λ to find the gradient.

Part 3 of 6Analysis

Analysis
Gradient
  • The gradient has units of V m and equals hc/e, which is approximately 1.24 × 10⁻⁶ V m.
Calculation
  • h = gradient × e / c, with e = 1.60 × 10⁻¹⁹ C and c = 3.00 × 10⁸ m/s.
Trend
  • Shorter wavelength LEDs, such as blue, need higher threshold voltages than red LEDs.
Intercept
  • A line through the origin supports the relation, and a non-zero intercept suggests systematic error.
LED colourTypical wavelength (nm)Threshold V (V)
Blue4702.64
Green5252.37
Yellow5902.11
Red6301.97

Part 4 of 6Sources of Error and Improvements

Judging first glow
  • The eye is subjective, so use a dark tube or a light sensor to reduce uncertainty.
LED wavelength
  • The stated wavelength is a peak value of a spread, so the 1/λ values are uncertain.
Slow voltage change
  • Increase the voltage in small steps and from below the threshold to stop overshooting.
Repeat readings
  • Averaging several readings for each LED reduces random error.

Part 5 of 6Worked Example

Question

  • An experiment gives a straight-line graph of threshold voltage V against 1/λ with gradient 1.24 × 10⁻⁶ V m.
  • Calculate the Planck constant.
  • (e = 1.60 × 10⁻¹⁹ C, c = 3.00 × 10⁸ m/s)

  1. Gradient = hc/e, so h = gradient × e / c.
  2. h = (1.24 × 10⁻⁶ × 1.60 × 10⁻¹⁹) / (3.00 × 10⁸).
  3. h = 1.984 × 10⁻²⁵ / 3.00 × 10⁸ = 6.61 × 10⁻³⁴ J s.

Answer h = 6.6 × 10⁻³⁴ J s.

Part 6 of 6Exam Checklist & Tips

4.11.3 – Key Points for the Exam

  • Light-emitting diode A semiconductor device that gives out light when current passes through it in the forward direction.
  • Threshold voltage The smallest voltage across an LED at which light is just emitted.
  • Gradient The slope of the V against 1/λ graph, equal to hc/e.
  • Planck constant The constant h that links a photon's energy to its frequency.
  • Systematic error A consistent error that shifts all readings in the same direction.

Common Mistakes

  • Plotting V against λ instead of 1/λ, which does not give a straight line.
  • Forgetting to convert wavelengths from nanometres into metres.
  • Using the supply voltage and not the voltage measured across the LED.
  • Saying the line gradient is h; it is hc/e.

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