The **Energy of Light **involves the use of a new variable *Planck's Constant*.

Light as Particles

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concept

## The Energy of Light

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here, we're going to say that the physicist Max Plank and Albert Einstein theorized that light was made of packets off or particles of electromagnetic radiation. Now we're going to say that this light, particle or packet are referred to as a photon, and if we're talking about a cluster of them, we can also use the term quantum now to calculate its energy. We use Plank's constant when it comes to light, and it uses the variable H and it's equal to 6.626 times 10 to the negative. 34 jewels, times seconds. So just keep in mind when we're looking for the energy of light, we're gonna incorporate Plank's constant. So now that we know this, click on to the next video and let's take a look at some formulas that are important when calculating the energy of life.

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concept

## The Energy of Light

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So when it comes to calculating the energy of light in the form of ah photon, we have two different formulas that we can rely on and realize only one of them has a purple box around it, so that one is the more commonly used formula. And that's the one you should keep in mind and memorize. So we're gonna say here the first version is used when we deal with energy and frequency. So here is going to say that change in energy or energy of a photon in jewels per photon equals plank's constant, which is H times frequency, which is, in seconds, inverse or hurts. Remember, frequency uses the same on Greek symbol mu. Now the other one we use when we're dealing with calculating the energy of a photon when given energy and wavelength. In this one, we're gonna say changing energy or energy of a photon in jewels over photons equals planes constant still. But now it's times the speed of light, divided by wave length in meters. So just remember two different formulas, one we use when we're dealing with frequency and energy, and the other one we use when we're dealing with wavelength and energy. Now, from the equations realized that this tells us that energy is directly proportional to frequency, meaning that if your energy is going up, your frequency is going up and it would be inversely proportional inversely proportional toe wavelength. That means that if your energy or frequency are increasing, that means wavelength would happen. The would have to be decreasing. So just keep in mind the relationships that we have between now energy, frequency and wavelength.

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example

## The Energy of Light Example 1

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here we're told to calculate the energy of a photon with the wavelength of to 93. m. Here they're giving us wavelength off the photon and they're asking for energy. So we're gonna use the second formula. Were the energy of a photon equals plank's constant times the speed of light divided by our wavelength. Here, Plank's constant is 6.626 times 10 to the negative, 34 jewels. Time seconds. Speed of light is 300 times 10 to the 8 m per second. And then we have our wavelength, which is to 93.7 m here. Seconds. Cancel out with seconds meters. Cancel out with meters. That leaves us jewels as our remaining unit. But remember, this is Jules per photon. So here this comes out to 6.768 times 10 to the negative 28 jewels per photon. Here are value has four sig figs because our to 93. m given to us initially also has four significant figures

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## The Energy of Light

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Now, up to this point, we know how to calculate the energy off. One photon on. We know unity would be jewels for photon. Now, in order to find the energy for Mullah photons, we can use the conversion factor with avocados number. Now here, the conversion factor would be one mullah Photons equals 6.22 times 10 to the 23 photons. So we know that that value represents avocados number. So just remember, when we calculate the jewels per photon from our formulas, we can use avocados number to convert it into jewels per mole of photons. Now we know this connection. Move onto the next video and let's put it to work.

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example

## The Energy of Light Example 2

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here. It says to calculate the energy for mobile photons with the frequency off 4.29 times 10 to the 15 seconds inverse. All right, so what we're gonna have here is we have energy and they're giving us frequency. So we're gonna say here energy of a photon equals plank's constant times frequency. So that's gonna be 6.626 times 10 to the negative. 34 jewels. Time seconds. That's plank's constant times are frequency in seconds in verse. Okay, so here's seconds we cancel out with inverse seconds when we get initially is 2.84 to 554 times 10 to the negative. 18 jewels per photo. Remember, we don't want to round until the very end. So now that we have jewels per photon realized, we need to find it in terms of moles of photons. So we're gonna use our conversion factor. So we're going to say here that we have, for every one mole of photons, we have 6.22 times 10 to the 23 photons. So here photons cancel out, and I'll have my answer in jewels per mole of photons. So this comes out to 1.7 one times 10 to the six jewels per mole of photons. Okay, so now our answer here has 366 Because our initial value also had 366

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Problem

Calculate the energy (in nJ) of a photon emitted by a mercury lamp with a frequency of 6.88 x 10^{14} Hz.

A

5.46 x 10

^{-9}nJB

9.89 x 10

^{-9}nJC

2.89 x 10

^{-10}nJD

4.56 x 10

^{-10}nJ7

Problem

A light ray has a wavelength that is 835 µm contains 6.32 x 10^{-3} J of energy. How many photons does this light ray have?

A

7.98 x 10

^{18}photonsB

4.85 x 10

^{19}photonsC

9.48 x 10

^{18}photonsD

2.65 x 10

^{19}photons8

Problem

How much energy (in kJ) do 4.50 moles of photons contain at a wavelength of 705 nm?

A

2.58 x 10

^{2}kJB

7.64 x 10

^{2}kJC

8.45 x 10

^{2}kJD

5.89 x 10

^{2}kJAdditional resources for The Energy of Light

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