Studying the experimental data, Max Planck developed a formula that explained what was happening in that blackbody. Using things commonly understood, like entropy and thermodynamics, as well as some concepts not understood at all, Planck introduced a concept of quantized energy, or energy that came in discrete packets. This certainly was a paradigm shift in the scientific thinking of the day. His theories were not generally accepted until later, when more experimentation showed the concept of light as a photon. Even Planck himself pursued ways to explain the blackbody radiation results using classical physics. Watch this video to see how the concept of quantization of energy was formulated.
Up to this point in the course, we've examined electromagnetic radiation, such as visible light, as a wave. But some behaviors of light can't be explained by wave behavior alone. This is what gave rise to quantum theory. So let's begin by looking at the dual nature of light. We've already seen how many of light's attributes are wave-like. For example, light exhibits, interference patterns, both constructive and destructive. Additionally, light diffracts, meaning it can bend around walls or radiate outward after passing through a narrow slit.
These behaviors gave scientists the impression that light was strictly a wave. However, around the turn of the century, physicists Max Planck and Albert Einstein made an important discovery. They proved that light also exhibits attributes that make it more like a particle than a wave. This particle nature is best seen through the photoelectric effect. See, when you shine a light on a sheet of metal, electrons are released.
Now, if light were purely wave-like in nature, then a brighter light would carry more energy, just like a louder sound does. But when the physicists actually measured the effect, they observed something different. They noted that a brighter light releases more electrons but only a higher frequency of light. That is to say, a light with a shorter wavelength releases electrons with greater kinetic energy.
This demonstrated that there was some type of particle, a photon, that was delivering packets of energy large enough to allow electrons to be released. This finally brings us to the idea of the quantum. For our purposes, quanta are like packets or bundles of energy. You either take the whole packet or none of it. And that's what it means for a value to be quantized because the defining characteristic of a quantum is that it cannot be subdivided at all.
In this sense, and this really gets to the particle nature of what we're examining, these are kind of like atoms. You can have one atom, you can have 3 million atoms, but you can't have half of an atom or 3.825 atoms.
As mentioned earlier, a quantum of electromagnetic energy is called a photon. Photons are in constant motion, always traveling at the speed of light, abbreviated as c, which is about 3 times 10 to the 8 meters per second. That's the fastest possible speed in the universe. So that's pretty quick. Because it's in constant motion, all of the photons' energy is kinetic energy.
Now, this seems counterintuitive because photons don't have mass, so how can they have kinetic energy? Well, let's look into that and see where their kinetic energy comes from. So we've seen how light energy comes in packets called photons, and we know that some of those photons are more energetic than others. But how exactly do we quantify this energy?
Well, as we saw earlier, the energy of a photon is determined by its frequency. The equation to find the energy of a photon is E equals hf, where E is the energy of the photon, measured in joules. h is a value called Planck's constant, and that number is always going to be 6.63 times 10 to the negative 34 joule-seconds. That is an extremely small number. And lastly, f is the frequency of the electromagnetic radiation, the light, and that's measured in hertz.
And this is why higher frequency light emitted more energetic electrons when it was shown on the metal sheet. That higher frequency light meant that the sheet was being bombarded with very high kinetic energy photons. Those photons were bumping into electrons and setting them free with a lot of kinetic energy. This is what solidified quantum theory, this realization that light particles were delivering these quantized values of very small energy to these electrons.
Now, because the energy values we will encounter in these interactions are so small, we'll often use a unit called the electronvolt, abbreviated eV, instead of the much larger unit of the joule. Fortunately, we can quickly convert between the two units using the conversion factor 1 electronvolt is equal to 1.6 times 10 to the negative 19 joules. To see how we can apply this information, let's quickly look at a couple of examples.
The first example reads, the frequency of violet light is 7.5 times 10 to the 14 hertz. How much energy does a photon of violet light carry? Well, to find the energy, we'll need to use the equation E equals hf. h is Planck's constant, 6.63 times 10 to the negative 34 joule seconds. Frequency, f, is given to us as 7.5 times 10 to the 14 hertz. Multiplying those values together gives us an energy of 4.97 times 10 to the negative 19 joules. That is an extremely small number.
So let's convert it into electronvolts. To do that, we multiply this value by the conversion factor of 1 electron volt per 1.6 times 10 to the negative 19 joules. And we find that our energy is 3.1 electronvolts. Let's look at one more example. This one reads, a photon has an energy of 6.2 electronvolts. What is the frequency of the photon?
Well, let's begin by getting this value into joules by multiplying by the conversion factor 1.6 times 10 to the negative 19 joules per 1 electronvolt. That gives us an energy of 9.92 times 10 to the negative 19 joules. Now we can plug that value, along with Planck's constant, into our photon energy equation, E equals hf.
That gives us 9.92 times 10 to the negative 19 joules is equal to Planck's constant, 6.63 times 10 to the negative 34 joules seconds times frequency f. Dividing both sides by Planck's constant reveals that the frequency of this photon is 1.5 times 10 to the 15 hertz, which is an ultraviolet photon, just like the ones that will give you a sunburn when you go outside.
Question
Why was the fact that photons were discrete packets of energy not discovered prior to the blackbody radiation experiment?
Because the discrete amount is so small that it was virtually impossible to determine until we were able to measure atomic-size measurements.
