The formula for it is momentum is equal to Planck's constant divided by the wavelength of a photon.

Now for those of you who want to see the derivation for the formula, it starts from this equation.

E squared is equal to the rest mass of a photon times c squared squared plus the momentum times c squared.

Now a photon is defined as not having any rest mass.

So this is zero.

It does have effective mass, but not any rest mass.

So we get this.

Now if we take the square root of both sides, we get that the energy of a photon is equal to the momentum times the speed of light.

Dividing both sides by c, we get that E over c is equal to the momentum.

Now E is equal to hf, it's Planck's constant times the frequency.

And keep in mind the speed of light is equal to the wavelength of a photon times its frequency.

So if we were to isolate lambda, it would be c over f.

If we were to raise both sides to the negative one, we get that f over c is one over lambda.

So we can write this as h times f over c and then replace f over c with what we have here.

So h times one over lambda.

So we get that the momentum of a photon is Planck's constant divided by the wavelength.

So whenever the wavelength of a photon changes, the momentum of that photon will change as well.

So to finish this problem, let's replace h with this value, 6.626 times 10 to the negative 34 joules times seconds.

And we're going to divide it by the wavelength.

So for part A, we have a 700 nanometer wavelength, or 700 times 10 to the negative 9 meters.

And so the momentum is going to be 9.466 times 10 to the negative 28 kilograms times meters per second.

So that's the momentum of a photon of red light.

Now what about part B?

What is the momentum of a 350 nanometer photon of UV light?

So notice that the momentum has been reduced by a factor of 2.

What happens to the, I mean the wavelength was reduced by a factor of 2.

So what happens to the momentum of a photon if we reduce the wavelength?

Notice that it's on the bottom of the fraction.

Anytime you decrease the denominator of a fraction, the value of the whole fraction goes up.

So if you decrease the wavelength, the momentum is going to increase.

So let's use the same formula to calculate the new momentum.

So all we've got to do is change the wavelength from 700 to 350 nanometers.

Of course, we could simply double our first answer, and that will give us the same answer as well.

So this is going to be 1.893 times 10 to the negative 27 kilograms times meters per second.

So that's the momentum of the photon of UV light.

At 350 nanometers.

Now let's try this problem.

What is the effective mass of a 450 nanometer photon of blue light?

Now we could use this equation to get that answer.

Momentum is equal to Planck's constant divided by the wavelength.

Now we know that momentum is mass times velocity.

So when using this equation, this will be treated as effective mass times velocity.

The velocity of a photon is going to be the speed of light.

And that's going to equal Planck's constant times the wavelength.

So the effective mass is going to be, if we divide both sides by c, is Planck's constant divided by the wavelength times the speed of light.

So this is the formula that we could use to calculate the effective mass of a photon.

And notice that the only thing that can change here is the wavelength.

Planck's constant and the speed of light, they're both constant values.

So the only thing that changes is the wavelength.

As the wavelength of the photon increases, the effective mass of that photon decreases.

Anytime the wavelength goes up, the frequency of the photon goes down.

The energy that that photon carries goes down as well.

So now let's get the answer.

So we have Planck's constant, which is this number.

And then that's going to be divided by the wavelength, which is 450 nanometers, or 450 times 10 to the negative 9 meters.

And then times the speed of light, 3 times 10 to the 8 meters per second.

So let's go ahead and plug that in.

So we get this value for the effective mass, 4.908.

I guess we can round that to 4.91.

Times 10 to the negative 36 kilograms.

It's very, very, very, very small.

Very close to zero.

But that is the effective mass of a 450 nanometer photon of blue light.