4.5.1 Photons

In 1900 Planck discovered that electromagnetic energy could only exist in certain values - it appeared to come in quanta (little packets). This proposed that electromagnetic radiation had a particulate nature (tiny packets of energy) rather than a continuous wave. Einstein called these ‘packets’ photons.

Nowadays we have more of an understanding that we can use different models to describe electromagnetic radiation. E.g we can use the photon model to explain how electromagnetic radiation interacts with matter and the wave model to explain it’s propagation through space.

So, now we know a photon is like a little packet of energy. We also need to know that the energy of each photon is directly proportional to its frequency. We can use the following equation to show this:

E = hf

NOTE: E (energy of the photon) is in joules, f (frequency of electromagnetic radiation) is in Hz, and h is the Planck constant.

If we were to combine E = hf with the wave equation (c= fλ) we are able to express the energy of a photon in terms of its wavelength and the speed of light through a vacuum:

E = (hc)/λ

NOTE: It is important to note that this equation has both wave elements (λ) and particulate elements (the energy, E, of a photon).

From the equation E = (hc)/λ we can see that the energy of a photon (E) is directly proportional to its wavelength (λ) so the smaller the wavelength the larger the energy of the photon.

Okay so if we think about it, one joule is pretty big at the subatomic scale of the quantum level. To combat this, we use electronvolts (eV) when measuring energies at the quantum scale. The energy of 1eV is defined as the energy transferred to or from an electron when it moves through a potential difference of 1V. But what actually is the quantity of 1eV? Well, we know the work done on an electron is VQ (W=VQ=Ve (e standing for the elementary charge)). So…

W = 1V x 1.60 × 10^-19 C = 1.60 × 10^-19 J.

This means that 1eV is equal to 1.60 × 10^-19 J

Using LEDs

We need to know a little experiment with LEDs to determine a value for the Planck constant. We can do this by considering the energies of the photons they emit. LEDs convert electrical energy into light energy by emitting visible light photons (of a specific wavelength) when the p.d. across them is above a critical value. At this p.d., work is being done (this is given by W=VQ) - this energy is about the same energy as the emitted photon. 

Connect a voltmeter across an LED. Add a safety resistor next to the LED (outside the voltmeter connections) and connect the whole system to a variable resistor/potentiometer connected to a power supply to vary the p.d out. We can us the voltmeter to measure the minimum p.d. that is required to turn of the LED. Place a black tube over the LED to help show exactly when the LED lights up. Provided we know the wavelength of the photons emitted by the LED then we can determine the Planck constant because…

At the threshold p.d. the energy transferred by an electron in the LED (work done) is approximately the energy of the single photon…..

W = VQ = Ve = E = hf = (hc)/λ…………. Ve=(hc)/λ

To obtain a more accurate result we can use a variety of LEDs that emit a known wavelength of photons then we can plot a graph of V against 1/λ. The gradient will be (hc)/e.