Light as a Particle
Learning Objectives: After this lesson, you should be able to…
- Calculate the frequency or wavelength of a photon, the energy of one photon and a mole of photons, the total energy (or the number) of multiple photons.
So far we have seen light as a wave, but there are three phenomena that are inconsistent with the wave nature of light:
- Blackbody radiation
- Photoelectric effect
- Line spectra
Blackbody radiation is the electromagnetic radiation emitted from a black body. At sufficiently high temperatures, this radiation is in the form of visible light. You've probably observed this when you heat the element on your stovetop. The sun and hot lava are other examples of blackbodies.
Classical physics would predict that as the temperature of a blackbody increases, the intensity of energy would increase infinitely as the wavelength emitted decreases. Lucky for us, our stove tops don't emit gamma rays or X-rays! In reality, as temperature increases a shift to shorter (more blue) wavelengths occurs and a maximum intensity is reached before tapering off. If you're ever looking at hot coals or even stars, the color can tell you something about the temperature. Red is going to have a longer wavelength and therefore a lower temperature. As temperature increases, we shift to shorter wavelengths and observe colors such as orange, white, and eventually blue (hottest).
The classical model doesn't explain the experimental data! Max Plank worked to develop a model that explained the experimental observations. Planck proposed light was composed of small particles known as photons and their energy was proportional to their frequency (rather than intensity). That energy is defined by the equation E=nhν. In this equation, E is the energy of n photons (where n is an integer) of identical frequency ν. The equation also involves a constant, h, known as Planck’s constant, which equals 6.626 x 10 J*s (a very small number). An important consequence of this equation is that the energy of a photon increases as frequency increases (E is proportional to ν). Since wavelength and frequency are inversely related (c=λν), the energy (E) of a photon increases as its wavelength decreases (E is inversely proportional to λ). Therefore gamma rays have the highest energy, the shortest wavelength, and the highest frequency of any type of electromagnetic radiation.
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A few years after Plank's proposal, Albert Einstein was studying the photoelectric effect. The photoelectric effect is the observation that many metals emit electrons when light is shone on them. The classical wave model would predict that electrons would be emitted as the intensity of light increased. For example, one could increase the brightness of low energy light and once enough energy was accumulated by the material, electrons would be ejected. However, Einstein observed that no matter how long a low-energy light was shone on a material, electrons were not emitted. What he actually observed was that a minimum frequency was required to eject the electrons. In looking at Figure 2 below, we can see that red light (low frequency) does not eject electrons. Upon increasing the frequency to green light, the ejection of electrons is observed. If the frequency is sufficiently high (i.e. blue light), any "extra" energy will be transferred to the electron in the form of kinetic energy and result in faster moving electrons. Einstein's experiments agreed with Plank's proposal that light was made of small particles and supported the wave-particle duality of light.
Last, the observation of line spectra also supported the particle-like nature of light. Light emitted from exited atoms only came in a few discrete frequencies. If light was purely a wave, one would expect to observe white light emitted from atoms (a continuous spectrum composed of all frequencies). We will see examples of line spectra in the next lesson.
You do not need to know the details of the experiments explained above, but you should be familiar with conclusions that were drawn (i.e. energy is proportional to frequency) and that they did not support the wave-like nature of light.
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