Now you might be wondering, what is blackbody radiation?

Well, any object with a temperature above 0 Kelvin is going to emit some form of electromagnetic radiation.

As the temperature increases, the energy of that radiation will increase as well.

So imagine if you have a metal, and you heat the metal.

As the temperature of the metal goes up, eventually, you'll notice that the metal will have a reddish glow to it.

And as you continue to heat up the metal, as the temperature increases, it's going to appear yellow, and then maybe even whitish.

Whenever you increase the temperature of an object, the molecules in that object will vibrate with more energy.

And the oscillations of the electric charges in those molecules can emit electromagnetic radiation.

So let's say you have an atom.

Let's say this is a hydrogen atom.

This is the first energy level.

The second energy level.

Let's say this is the third energy level.

When an electron in this atom, when it absorbs energy, it can jump to a higher energy level.

Now, when that electron returns to its original state, or if it drops to a lower energy level, it's going to emit electromagnetic energy.

And so as these electrons, as they oscillate back and forth, they can absorb and emit electromagnetic energy.

Now, the energy that is carried by a photon is a multiple of this value, hf.

So we're going to put an n, where n is an integer, h is the Planck's constant, f is frequency.

The frequency is measured in hertz, or s to the minus 1, and h is Planck's constant, which is 6.626 times 10 to the negative 34 joules times seconds.

Now, this equation tells us something very important, and that is that the energy of a photon is quantized.

It's not continuous, it can only have discrete values.

So it can't be just any value, but it's a multiple of hf.

It can be 1hf, it can be 2hf, 3hf, but nothing in between that.

So the energy of a photon can only exist in discrete values, it can't take any value.

So thus we could say that energy is quantized.

Now let's work on some problems.

Calculate the energy of a photon with a frequency of 4 times 10 to the 14 hertz.

So we could use this formula to get the answer.

So we're only dealing with a single photon, so n is going to be 1.

Planck's constant, that's 6.626 times 10 to the negative 34, and this is joules times seconds.

The frequency is 4 times 10 to the 14 hertz.

And hertz is seconds to the minus 1, or 1 over seconds.

And so we can see the unit, seconds, will cancel.

And this is going to leave behind the unit joules.

And so the energy is going to be 2.65 times 10 to the negative 19 joules.

So that's the energy of this particular photon.

Now what is the energy of a red photon with a wavelength of 700 nanometers?

Whenever light has a wavelength of about 700 nanometers, it's going to appear red.

Now, in order to do this one, we need an additional formula.

The wavelength of light times frequency is equal to the speed of light.

So what we need to do first is we need to calculate the frequency.

The frequency is the speed of light divided by the wavelength.

And the speed of light, which is the same for all types of electromagnetic radiation in a vacuum, is 3 times 10 to the 8 meters per second.

The wavelength is 700 nanometers, and a nanometer is 10 to the minus 9 meters.

So the unit meters will cancel.

Giving us the unit 1 over seconds, which is frequency in hertz.

So 3 times 10 to the 8 divided by 700 times 10 to the negative 9.

That's going to give us a frequency of 4.286 times 10 to the 14 hertz.

Now that we know the frequency, we can calculate the energy of the red photon.

So since we're only dealing with a single photon, and there's one, and then we have Planck's constant.

And then we have the frequency, 4.286 times 10 to the 14.

I'm going to write 1 over seconds for the unit.

So I got 2.84 times 10 to the negative 19 joules.

So that is the energy of a single red photon.

That's how you can calculate it.

Now, let's work on one more problem.

What is the energy of 5 blue photons with a wavelength of 450 nanometers?

So this problem is very similar to number 2.

The only difference is we have an n value of 5.

So let's begin by calculating the frequency.

The frequency is going to be the speed of light divided by the wavelength.

That's 3 times 10 to the 8 meters per second divided by 450 nanometers or 450 times 10 to the negative 9 meters.

So we're going to cancel the unit meters just like we did before.

So this works out to be 6.67 times 10 to the 14 hertz.

So now that we know the frequency, let's calculate the energy of the photon.

So E is equal to n h f. n is 5 since we're dealing with 5 photons, 5 blue photons. h is always going to be the same, Planck's constant.

That's not going to change.

So that's just a number you're going to have to commit to memory.

And we have a frequency of this value.

So 6.67 times 10 to the 14 times Planck's constant times 5 will give us this answer.

So the energy of the 5 blue photons combined is going to be 2.21 times 10 to the negative 18 joules.

So now you know how to calculate the energy of a single photon or a group of photons if you know the frequency of the photons or their wavelength.