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## Analytical Chemistry

Learn the toughest concepts covered in your Analytical Chemistry class with step-by-step video tutorials and practice problems.

17. Fundamentals of Spectrophotometry

# Properties of Light

The Nature of Light
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## The Nature of Light

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So in terms of the electromagnetic spectrum we said that we look at three variables energy, frequency and wavelength. Now in terms of frequency and wavelength, we're gonna say here that mu represents our frequency. It's the number of waves you have per second and it's using the units of seconds inverse or hurts. Then we're gonna say that lambda represents our wavelength. It's the distance from one crest of a wave to the other and expressed in units of meters here, if we take a look at a typical electromagnetic spectrum wave that's basically done on plane polarized light, we're gonna say here we have our Y axis, our Z axis and our X axis here. Here we're gonna say the top of this wave, the crest to the other wave would represent our wavelength lambda. Then we'd say here that the number of waves we get within a given second would represent my frequency or mu We'd say here that this here represents our electromagnetic wave and then here that's protruding out on the Y axis. This would represent our magnetic field vectors. Now the energy involved is directly proportional to frequency. So the more waves we get per second, the greater the energy would be. We can also say that the height of one wave would be our amplitude. Our amplitude does not directly influence the energy of our particular wave. Again, that is frequencies. Job. So these are the variables that you need to remember. This is how they're related to one another. Remember frequency and wavelength are inversely proportional. If there are several waves within a given second, the frequency will be high, but then the distance between those waves will be very small. So as your frequency is increasing, your wavelength has to be decreasing. Remember, they're connected to the energy of the different types of electromagnetic spectrum radiation that we saw up above.
Properties of Light
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example

## Properties of Light

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So here it says to calculate the wavelength in nanometers of the red light emitted by neon sign with a frequency of 4.16 times 10 to the eight megahertz. Alright, so they're asking us to determine wavelength which is represented by the variable lambda and frequency which is represented by mu. They're connected by the equation that speed of light equals frequency times wavelength. Here we're looking for wavelength so we need to isolate wavelength. So my wavelength equals speed of light divided by my frequency speed of light. Remembers 2.998 times 10 to the eight m per second, divided by your frequency in hertz, not megahertz. So we have to do some converting. So we have 4.16 times 10 to the eight megahertz. Remember here that one MHz is equal to 10 to the six hurts. That gives me 4.16 times 10 to the 14 Hz. Take that now and plug it in. So we have 4.16 times 10 to the 14 hertz hurts and seconds inverse are the same. So they're going to cancel out at this point. This will give me my wavelength in meters. So I get 7.21 times 10 to the negative seven m. But remember I didn't ask for the wavelength in meters, I asked for it in nanometers. So we need to do one last conversion to get to our final answer. We have 7.21 times 10 to the negative seven m For every one nanometer, it's 10 to the negative nine m. So meters cancel out. And what we get at the end is 721 nm as our final answer. So that number represents the wavelength of the red light that's being emitted by a neon sign. This answer is reasonable because it lies within the visible light spectrum of the electromagnetic spectrum 721 is around the range of red light. Now that we've seen. Example, one take a look at example to see if you can answer that final question here, we're asking for the energy of a mole of photons. So at this point, you should be able to at least calculate the energy of a single photon. If you don't know what to do after that. Don't worry, come back and see how I approach example, too.
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## Properties of Light

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So here it asks, what is the energy in jewels of a mole of photons associated with visible light of wavelength for 93 nanometers. Alright, what we're gonna do first is we're going to determine what the energy of a single photon is before we figure out the mole of photons. So we're gonna say the energy of a single photon equals planks constant times. Because the question is dealing with wavelength, we're gonna say times speed of light divided by wavelength. So plank's constant is 6.626 times 10 to the negative 30 for jules, times seconds. Speed of light is 2.998 times 10 to the eight m per second. And we need wavelength to be in units of m. So we have to convert the 493 nm into meters. So one nanometer is equal to 10 to the -9 m. So it gives me 4.93 times 10 to the -7 m, plug that in. So seconds cancel out meters, cancel out what we're going to get at this point is 4.29 times 10 to the negative 19 jewels per photon. Now we have to convert jewels per photon into jewels, per mole of photons. So bring down that value. We're gonna have to get rid of those photons. We're gonna say here one mole of photons just like one mole of anything is equal to avocados, number 6.22 times 10 to the 23 photons. So photons here cancel out. And I'll have as my final answer jewels per mole of photons, so that gives me 2.43 times 10 to the five jewels per mole. So realize we utilized the first equation in order to figure out the energy of a single photon, but then to convert it into molds a photon, we have to use avocados number. Remember that step in order to figure out the final answer for any question that appears like this.
Properties of Light Calculations
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## Properties of Light Calculations 1

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So here we're told laser pulse produces 1.242 killer jewels of energy. It was experimentally determined that the pulse contains 3.50 times 10 to the 22 photons determine the wavelength of light in meters emitted by one photon. Alright, so we're talking about energy and we're talking about wavelength. Remember the equation that connects them together is energy of a photon equals plank's constant times the speed of light divided by wavelength in meters. Now we're going to plug in the values that we know from the information given. We want to isolate our wavelength. So here if we rearrange this equation, we'll be able to isolate our wavelength. So wavelength equals planks, constant times speed of light, divided by the energy of a single photon, plug in plank's constant plug in speed of light. So when we do that, all we have to do now is determine what the energy of a single photon is. And plug that into. The formula were given what the total energy is. And we're told that total energy is the result of this many photons. So all we're gonna do here is we're gonna convert my total energy into jewels. So killer jewels cancel out. Now I have jewels and we're gonna divide that by the total number of photons so that we can figure out the energy of a single photon. So we have 1.242 times 10 to the three jewels total divided by the number of photons will give me the energy of a single photon. So there goes the energy of a single photon and we can take that and plug it into our formula. So here jules cancel out seconds, cancel out. We'll have a final answer here in meters. So when we plug all that in, we're gonna get 5.60 times 10 to the negative six m. So just realize for a question like this, the equation that connects wavelength and energy together is this one. But here the energy is of a single photon. So we have to take the total energy and divided by the number of photons to find out what that energy is. Once you do plug it in to isolate your wavelength at the end and meters. Now that you've seen this example, move on to example to look to see if you can determine what the final answer will be for this question. Don't overthink it. Read into what the question is asking you to find and then do any types of manipulations needed to get your final answer. Once you do move, move on and take a look at the video in which I explain how to approach. Example too
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