4.11.3 Determining the Planck Constant

• When a large enough potential difference is applied across a light-emitting diode (LED), it emits photons that all have the same wavelength and frequency
• When the LED just begins to glow, the energy, E, lost by each electron as it passes through the LED is converted into the energy of a single photon
• The energy, E, of a photon is equal to:

• Where:
  • f = frequency of the emitted photon (Hz)
  • λ = wavelength of the emitted photon (m)
  • h = Planck’s constant (J s)
  • c = speed of light (m s^–1)

• The energy lost by each electron is:

E = e∆V

• Where:
  • e = elementary charge (C)
  • ∆V = potential difference across the LED (V)

• Equating the two energies gives the equation:

• This equation can then be used to estimate the Planck's constant, h

The potential difference across an LED is proportional to the reciprocal of the wavelength of light emitted

Aims of the Experiment

The aim of this experiment is to use the I–V characteristics of different coloured LEDs to determine the value of the Planck constant

Variables

• Independent variable = wavelength of light emitted by the LED, λ
• Dependent variable = potential difference across the LED, ΔV
• Control variables:
  • E.m.f of the cell

Equipment List

• Note – ensure the LEDs have a clear, colourless casing surrounding the LED so that the colour of the light comes from the device itself and not from the coloured casing
• Resolution of measuring equipment:
  • Voltmeter = 1 mV
  • Ammeter = 0.1 mA

Method

1. Set up the circuit as shown in the diagram above. Connect the ammeter in series with the LED to measure the current through it and connect the voltmeter in parallel to the LED to measure the voltage across it
2. The applied voltage can be changed by using the potentiometer. Slowly increase the voltage in steps of 0.05 V from 0 V to 3 V until the LED just begins to emit light
3. Note down the threshold voltage ie. the minimum p.d across the LED that is required before any current is able to flow
4. Repeat the procedure for each coloured LED

• Record the results in a table similar to this:

Analysing the Results

• Comparing the equation eV = hc / λ with the equation of a straight line y = mx + c
  • y = ΔV (V)
  • x = 1 / λ (m^–1)
  • Gradient = hc / e

• Plot a graph of ΔV against 1 / λ for the different LEDs and draw a line of best fit
• This should produce a straight line with slope hc / e, as shown below:

• Measure the gradient and multiply it by e / c to determine Planck's constant, h

h = gradient × (e / c)

• Compare this experimental value of h with the accepted value and find the percentage error using:

Evaluating the Experiment

Systematic Errors:

• There is a human error associated with identifying the exact voltage at which the LED just begins to glow
  • For optimal results, use a black viewing tube in a darkened room
  • A more accurate method would be to plot a graph of current against voltage for each LED and determine the threshold voltage by extrapolating the straight line backwards until it intercepts the x-axis

Random Errors:

• LEDs do not emit a single frequency of light, instead, they emit a narrow spectrum with a width of approximately 60 nm
  • The wavelength quoted on the LED represents the central wavelength it emits
  • When the LEDs just begin to glow, the lower end of the wavelength will be emitted, so this can introduce an error in the wavelength

I–V characteristics for LEDs emitting red, orange, green and blue light

Safety Considerations

• Do not stare directly at LEDs when they are brightly lit, especially the blue LED
  • LEDs are safe when they just begin to glow, but they quickly become bright as the potential difference increases above the threshold value
  • As the blue LED is closest to the UV part of the spectrum, do not stare at the blue LED even when it is dimly lit

• LEDs can be destroyed if the current flowing through them is too large
  • The current should be no more than about 50 mA, but the exact limit can be checked on the ratings for the specific LEDs used
  • Note that when the current flowing through the LED is small, the LED might not light up, but the ammeter can still measure the current
  • Use a 330 Ω resistor to limit the current flowing through the LED

• The potentiometer can be destroyed if wired incorrectly, and this can be a fire hazard
  • An incorrectly wired potentiometer can create a short circuit which leads to a large potential difference across a low resistance
  • As a result, the potentiometer heats up rapidly and may begin emitting smoke

• If burning is smelled turn off the electricity supply immediately
• Make sure no water is present near any electrical equipment