SP Unit 2.7
Practicals
Photons
SP Unit 2.7PracticalsPhotonsLearners should be able to demonstrate and apply their knowledge and understanding of: |
|
|---|---|
| 1. | Determination of h using LEDs |
-
Determination of Planck’s Constant (h) Using LEDs
-
⇒ Objective:
- To determine the value of Planck’s constant (h) by measuring the threshold voltage of Light Emitting Diodes (LEDs) of different colors.
- ⇒ Apparatus Required:
- – LEDs of different colors (Red, Green, Blue, Yellow, etc.)
- – A variable DC power supply
- – A digital voltmeter
- – A microammeter
- – A resistor (~1 kΩ)
- – Connecting wires
- – A graph paper (for analysis)
- Figure 1 Determination of Planck’s Constant using LEDs
-
⇒ Theory:
- When a forward bias voltage (V) is applied to an LED, electrons recombine with holes in the semiconductor material, emitting photons of light. The energy of the emitted photon is given by:
- [math]E = hf[/math]
- Where:
- – E is the energy of the emitted photon (Joules),
- – h is Planck’s constant,
- – f is the frequency of the emitted light (Hz).
- The energy of the emitted photon is also related to the threshold voltage (V) of the LED:
- [math]E = eV[/math]
- Where:
- – e is the elementary charge of an electron ( [math][/math]),
- – V is the threshold voltage of the LED.
- By measuring V for different LEDs and knowing their corresponding wavelengths (λ), we can use the relation:
- [math]f = \frac{c}{\lambda}[/math]
- Where c is the speed of light ([math]3.0 \times 10^8 \, \text{m/s}[/math]), to calculate h.
-
⇒ Procedure:
- 1. Circuit Setup:
- – Connect the LED in series with a 1 kΩ resistor to limit the current.
- – Connect the voltmeter across the LED to measure its threshold voltage.
- – Connect the ammeter in series to measure the current.
- – Connect the variable DC power supply across the circuit.
- 2. Taking Readings:
- – Slowly increase the voltage from the power supply and note the threshold voltage (V) when the LED just starts to emit light.
- – Record the threshold voltage for different colored LEDs (each color corresponds to a specific wavelength).
- 3. Data Collection:
- – Note the wavelength (λ) of each LED from standard reference values.
- – Convert the wavelength into frequency using [math]f = \frac{c}{\lambda}[/math].
- 4. Calculation of Planck’s Constant:
- – For each LED, calculate h using the formula:
- [math]h = \frac{eV}{f}[/math]
- – Plot a graph of V (Y-axis) against [math]1/\lambda[/math] (X-axis).
- – The slope of the graph gives [math]hc/e[/math], from which h can be determined.
- Figure 2 a graph of V (Y-axis) against [math][/math] (X-axis)
- ⇒ Observations & Data Table:
| LED Color | Wavelength (λ) (nm) | Frequency (f) (Hz) | Threshold Voltage (V) | Planck’s Constant (h) (Js) |
|---|---|---|---|---|
| Red | 650 | [math]4.61 \times 10^{14}[/math] | 1.8 | To be calculated |
| Green | 520 | [math]5.77 \times 10^{14}[/math] | 2.2 | To be calculated |
| Blue | 470 | [math]6.38 \times 10^{14}[/math] | 2.6 | To be calculated |
-
⇒ Result:
- The calculated value of Planck’s constant should be approximately [math]h = 6.626 \times 10^{-34} \, \text{Js}[/math] with some experimental error.
-
⇒ Precautions:
- – Ensure proper polarity of the LED before applying voltage.
- – Increase the voltage gradually to avoid damaging the LED.
- – Use precise instruments to measure voltage and current.
- – Perform multiple trials and take the average to minimize errors.
-
⇒ Conclusion:
- By measuring the threshold voltage of different LEDs and their corresponding frequencies, we determined Planck’s constant (h) experimentally. The obtained value should be close to the accepted standard value with minimal error.