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# What is the Size of a Photon?

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Author: Jerry Silver

### The Idea

One of the pivotal discoveries of the twentieth century was the recognition that light is made of photons, which can be thought of as minute particles of light. Light behaves in many ways like a wave, but it also behaves in many ways as if it consisted of particles. Just how big (or small) are these particles of light?

### What You Need

• several LEDs (light-emitting diodes) of known wavelength
• variable power supply
• jumper wires
• voltmeter (or multimeter configured as a multimeter)
• dark room

### Method

The schematic for this experiment is shown in Figure 119-1.

1. Attach the positive end of the voltmeter to the positive end of the power supply, and the negative end of the voltmeter to the negative end of the power supply.
2. Adjust the power supply to give a reading of zero volts.
3. Select an LED. Use jumper wires to connect the positive side of the power supply to the positive terminal of the LED. (The positive terminal of the LED is the longer one.)
4. Connect the negative side of the power supply to the LED.
5. Darken the room.
6. Slowly increase the voltage from the power supply until the LED just begins to give off light. For visible light, this will be between 1.2 volts and 2.5 volts.
7. Write down the voltage that results in light just being produced.
8. Repeat this process for all the LEDs you have.
9. Make a graph of voltage versus frequency.

### Expected Results

The higher the frequency, the higher the voltage needed to turn on the LED. The relationship is linear, as shown in Figure 119-2.

### Why It Works

According to quantum theory, the energy of a photon depends on its frequency. Higher frequency light (or light closer to the blue side of the visible spectrum) has more energy. Lower frequency light (closer to the red side) has less energy. For a photon of a given frequency, f, or color, the energy is given by hf, where h is called Planck's constant.

### Other Things to Try

The amount of energy needed to turn on an LED is given by qV, where q is the charge of an electron = 1.6 × 10–19 C and V is the applied voltage. From the slope of the graph, you can estimate Planck's constant (from the slope of the previously plotted equation, v = (h/q)f ). Planck's constant can be determined by dividing the slope of the graph by the charge of an electron. The accepted value for Planck's constant is 6.63 × 10–34 J-s. The slope of the graph in Figure 119-2 is about 7 × 10–34 J-s, which provides a reasonable order of magnitude estimate of Planck's constant.

So how small is a photon? Let's take a 60W light. This means that at about 5 percent efficiency, there are about 3 Joules of energy coming from the bulb every second. According to Planck's constant this means that every second 3 J /6.63 × 10–34 J-s = 4.5 ×1033 photons are coming from the light bulb. This incredibly large number of photons gives an idea of the extremely small size of the photon.

### The Point

The turn-on voltage for an LED gives an indication of how much energy is contained in a single photon. Photons with higher frequency (shorter wavelength) have more energy than photons with lower frequency.