Determining Planck's constant using LEDs

Practical method

Aim

Determine the Planck constant from the threshold p.d. of LEDs of different colours.

Variables

Independent variable: LED wavelength
Dependent variable: threshold (striking) p.d.
Control variables: the same circuit; the same criterion for 'just lit'.

Apparatus

• LEDs of known wavelength (blue, green, yellow, red)
• Potential divider supply
• Voltmeter
• Protective resistor
• Dark tube to view the LED

Method

1. Connect each LED with a protective resistor to a potential divider, with a voltmeter across the LED.
2. Slowly increase the p.d. until the LED just begins to glow (viewed through a dark tube); record the threshold p.d. V.
3. Repeat for each LED and take repeat readings.
4. At threshold, eV = \(\dfrac{hc}{\lambda }\). Plot V against \(\dfrac{1}{\lambda }\): gradient = \(\dfrac{hc}{e}\).

Sample results

Wavelengths from the manufacturer's data.

Analysis

V against \(\dfrac{1}{\lambda }\) is a straight line with gradient 1.24 × 10⁻⁶ V m. h = \(\dfrac{\text{gradient} \times e}{c}\) = \(\dfrac{1.24 \times 10^{-6} \times 1.60 \times 10^{-19}}{3.00 \times 10^{8}}\) = 6.6 × 10⁻³⁴ J s, close to the accepted Planck constant.

Uncertainty

Judging the 'just lit' point varies between observers by about ±0.05 V (2%). LEDs emit a band of wavelengths (±10 nm), adding about 2%.

Errors and improvements

Risk assessment

Common mistakes

• Measuring the p.d. across the whole circuit.
• Forgetting to convert nm to m.
• Using V against λ instead of \(\dfrac{1}{\lambda }\).

Worked analysis

Green LED: h = \(\dfrac{eV\lambda }{c}\) = \(\dfrac{1.60 \times 10^{-19} \times 2.36 \times 525 \times 10^{-9}}{3.00 \times 10^{8}}\) = 6.61 × 10⁻³⁴ J s.

Common misconception

At threshold, the energy one electron gains crossing the LED (eV) is roughly the energy of one emitted photon (hf), which is why different colours need different p.d.s.