Properties of Light PDF

View this QuickTake in the app Properties of Light Modified: Sep 17, 2024 9:02 PM 1. Outline Outline: Properties of Light Lecture Introduction Overview of light’s dual nature as waves and particles....

View this QuickTake in the app Properties of Light Modified: Sep 17, 2024 9:02 PM 1. Outline Outline: Properties of Light Lecture Introduction Overview of light’s dual nature as waves and particles. Historical Theories of Light 1. Wave Theory Proposed by Christiaan Huygens. Supported by diffraction patterns and experiments. 2. Particle Theory Suggested by Sir Isaac Newton. Concept of light consisting of particles called corpuscles. Characteristics of Light Waves 1. Wavelength (λ) Definition: Distance between two consecutive points of a wave. Measurement: Typically in nanometers for visible light. 2. Amplitude Definition: Height of the wave from the middle line. Indicates the intensity of the wave. 3. Frequency (ν) Definition: Number of cycles passing through a point per second. Measurement: In Hertz (Hz). Relationship Between Wavelength and Frequency Inverse Relationship As wavelength increases, frequency decreases, and vice versa. Speed of Light (c) Constant speed in a vacuum: (3 \times 10^8) meters per second. Equation: (c = \lambda \nu). Electromagnetic Spectrum Visible Spectrum Range: 400 to 700 nanometers. Only part visible to the human eye. Other Regions Infrared, microwaves, radio waves (low frequency). Ultraviolet, X-rays, gamma rays (high frequency). Quantum Theory of Light 1. Planck’s Hypothesis Introduced by Max Planck. Light emitted in discrete packets called photons. 2. Planck’s Constant (h) Value: (6.626 \times 10^{-34}) joules per second. Energy calculation: (E = h \nu). Photoelectric Effect Einstein’s Contribution www.quicktakes.io Properties of Light Page 1/9  View this QuickTake in the app Shining ultraviolet light on metals ejects electrons. Demonstrates light’s particle nature. Bohr Model of the Atom Quantized Energy Levels Proposed by Niels Bohr. Electrons occupy specific orbitals with quantized energy levels. Electrons transition by absorbing or emitting energy as photons. de Broglie Hypothesis Wave-Particle Duality Suggested by Louis de Broglie. All matter exhibits wave-like properties. Wavelength inversely proportional to mass and velocity. Heisenberg’s Uncertainty Principle Observation Limitations Proposed by Werner Heisenberg. One cannot simultaneously know the exact position and momentum of an electron. Observing an electron alters its state. Calculations and Examples Wavelength and Frequency Using the speed of light equation to find missing values. Energy of Photons Calculating energy using Planck’s constant and frequency. Rydberg Equation Used to calculate the wavelength of light emitted during electron transitions in hydrogen atoms. Practical Applications Spectroscopy Identifying elements based on their emission spectra. Radiation Understanding how objects emit electromagnetic waves. Visible as color when heated. Summary Detailed exploration of light’s properties. Emphasis on dual nature and historical/modern theories. Coverage of fundamental concepts: wavelength, frequency, amplitude, electromagnetic spectrum. Introduction to quantum mechanics principles: Planck’s hypothesis, photoelectric effect, Bohr model. Advanced topics: de Broglie’s wave-particle duality, Heisenberg’s uncertainty principle. Supported by practical calculations and examples. 2. Study guide Study Guide: Properties of Light Summary This lecture explores the dual nature of light, examining its behavior as both waves and particles. It covers historical theories, fundamental characteristics, and modern quantum mechanics principles. Key topics include the wave and particle theories of light, the electromagnetic spectrum, Planck’s hypothesis, the photoelectric effect, the Bohr model, de Broglie’s wave-particle duality, and Heisenberg’s uncertainty principle. Practical applications such as spectroscopy and radiation are also discussed. Key Topics www.quicktakes.io Properties of Light Page 2/9  View this QuickTake in the app Historical Theories of Light 1. Wave Theory: Proposed by Christiaan Huygens, supported by diffraction patterns. 2. Particle Theory: Suggested by Sir Isaac Newton, describing light as particles (corpuscles). Characteristics of Light Waves 1. Wavelength (λ): Distance between two consecutive points of a wave, measured in nanometers (nm) for visible light. 2. Amplitude: Height of the wave from the middle line, indicating intensity. 3. Frequency (ν): Number of cycles passing through a point per second, measured in Hertz (Hz). Relationship Between Wavelength and Frequency Inverse Relationship: ( \lambda \uparrow \Rightarrow \nu \downarrow ) and vice versa. Speed of Light (c): Constant speed in a vacuum, (3 \times 10^8) meters per second. [ c = \lambda \nu ] Electromagnetic Spectrum Visible Spectrum: 400 to 700 nm, visible to the human eye. Other Regions: Infrared, microwaves, radio waves (low frequency), ultraviolet, X-rays, gamma rays (high frequency). Quantum Theory of Light 1. Planck’s Hypothesis: Light emitted in discrete packets called photons. 2. Planck’s Constant (h): (6.626 \times 10^{-34}) joules per second. [ E = h \nu ] Photoelectric Effect Einstein’s Contribution: Demonstrated light’s particle nature by showing that ultraviolet light ejects electrons from metals. Bohr Model of the Atom Quantized Energy Levels: Electrons occupy specific orbitals and transition between levels by absorbing or emitting photons. de Broglie Hypothesis Wave-Particle Duality: All matter exhibits wave-like properties. [ \lambda = \frac{h}{mv} ] Heisenberg’s Uncertainty Principle Observation Limitations: One cannot simultaneously know the exact position and momentum of an electron. [ \Delta x \Delta p \geq \frac{h}{4\pi} ] Calculations and Examples Wavelength and Frequency Using the speed of light equation: [ c = \lambda \nu ] Energy of Photons Calculating energy using Planck’s constant: [ E = h \nu ] Rydberg Equation Used to calculate the wavelength of light emitted during electron transitions in hydrogen atoms: [ \frac{1}{\lambda} = R \left( \frac{1} {n_1^2} - \frac{1}{n_2^2} \right) ] where ( R ) is the Rydberg constant. Practical Applications www.quicktakes.io Properties of Light Page 3/9  View this QuickTake in the app Spectroscopy: Identifying elements based on their emission spectra. Radiation: Understanding how objects emit electromagnetic waves, visible as color when heated. Summary The lecture provides a detailed exploration of light’s properties, emphasizing its dual nature and the historical and modern theories that explain its behavior. It covers fundamental concepts such as wavelength, frequency, amplitude, and the electromagnetic spectrum, along with quantum mechanics principles like Planck’s hypothesis, the photoelectric effect, and the Bohr model. The lecture also introduces advanced topics like de Broglie’s wave-particle duality and Heisenberg’s uncertainty principle, supported by practical calculations and examples. 3. Glossary Historical Theories of Light Wave Theory: Christiaan Huygens proposed that light behaves as waves, supported by diffraction patterns and experiments. Particle Theory: Sir Isaac Newton suggested that light consists of particles called corpuscles. Characteristics of Light Waves Wavelength (λ): The distance between two consecutive points of a wave, typically measured in nanometers for visible light. Amplitude: The height of the wave from the middle line, indicating the intensity of the wave. Frequency (ν): The number of cycles passing through a point per second, measured in Hertz (Hz). Relationship Between Wavelength and Frequency Inverse Relationship: As wavelength increases, frequency decreases, and vice versa. Speed of Light (c): The constant speed of light in a vacuum is (3 \times 10^8) meters per second, given by the equation (c = \lambda \nu). Electromagnetic Spectrum Visible Spectrum: Ranges from 400 to 700 nanometers, the only part of the spectrum visible to the human eye. Other Regions: Includes infrared, microwaves, radio waves (low frequency), and ultraviolet, X-rays, gamma rays (high frequency). Quantum Theory of Light Planck’s Hypothesis: Max Planck introduced the idea of quantized energy levels, where light is emitted in discrete packets called photons. Planck’s Constant (h): (6.626 \times 10^{-34}) joules per second, used to calculate the energy of photons (E = h \nu). Photoelectric Effect Einstein’s Contribution: Albert Einstein explained that shining ultraviolet light on metals ejects electrons, demonstrating light’s particle nature. Bohr Model of the Atom Quantized Energy Levels: Niels Bohr proposed that electrons occupy specific orbitals with quantized energy levels. Electrons transition between levels by absorbing or emitting energy as photons. de Broglie Hypothesis Wave-Particle Duality: Louis de Broglie suggested that all matter exhibits wave-like properties, with wavelength inversely proportional to mass and velocity. Heisenberg’s Uncertainty Principle Observation Limitations: Werner Heisenberg stated that one cannot simultaneously know the exact position and momentum of an electron, as observing it alters its state. www.quicktakes.io Properties of Light Page 4/9  View this QuickTake in the app Calculations and Examples Wavelength and Frequency: Using the speed of light equation to find missing values. Energy of Photons: Calculating energy using Planck’s constant and frequency. Rydberg Equation: Used to calculate the wavelength of light emitted during electron transitions in hydrogen atoms. Practical Applications Spectroscopy: Identifying elements based on their emission spectra. Radiation: Understanding how objects emit electromagnetic waves, visible as color when heated. 4. Practice Explain the wave theory of light as proposed by Christiaan Huygens and provide an example of an experiment that supports this theory. Describe Sir Isaac Newton’s particle theory of light and discuss how it differs from the wave theory. Define wavelength ((\lambda)) and explain how it is measured for visible light. What is the relationship between the amplitude of a light wave and its intensity? Using the equation (c = \lambda \nu), calculate the frequency of light with a wavelength of 500 nm. List the different regions of the electromagnetic spectrum and identify which part is visible to the human eye. Explain Planck’s hypothesis and how it led to the concept of photons. Calculate the energy of a photon with a frequency of (5 \times 10^{14}) Hz using Planck’s constant. Describe the photoelectric effect and how Einstein’s explanation supports the particle nature of light. Using the Rydberg equation, calculate the wavelength of light emitted when an electron in a hydrogen atom transitions from the (n=3) level to the (n=2) level. 5. Transcript In this video we’re going to look at properties of light. So when we think of light, you probably remember diffraction patterns you’ve seen when people did light experiments where you shine light onto the surface of something and you can see the reflection of the light in waves and you can see dark places where the light is blocked. You can even see these diffraction patterns if you have barriers to the light. So this suggested that light moves in waves. It creates a pattern. In the 1700s, there were two ideas about the nature of light. The first was that light worked as waves, as we see in the picture. The second was that light worked as tiny little particles. And Sir Isaac Newton called these corpuscles. Light moves as a stream of corpuscles. But Christiana Huygens, who took up a lot of these experiments from Maxwell about the waves coming from light, insisted that light was made of waves. So two different theories. Light is made of particles or corpuscles, or light is made of waves. And there were a lot more experiments designed around the idea of light moving as waves. So more data supported this idea. So we’re going to look at waves first. And waves of light are very much like we think of waves on the water. We have to describe a few different characteristics of waves. So waves are a repeated disturbance that occurs at regular intervals of time and distance. And we can change those intervals. We can make the waves have longer time between them or bigger distance between them, or we can make it shorter. So to describe waves, we have to describe a few characteristics. The first is wavelength. Wavelength describes the distance between two consecutive waves. so taking the same point on two consecutive waves and measuring the distance between them and you can take the distance at any two of the same points of adjacent waves so we can measure any of these and we would get the same distance so this is denoted as wavelength which is this lambda wavelength is measured as a distance typically in nanometers when we’re talking about visible light, but we can do it in any distance, meters, kilometers will work as well. The other idea that we need to look at for waves is amplitude. Amplitude is this vertical distance from an imaginary middle line. According to the definition, it’s half the distance between the minima and the maxima. So if we imagine the straight line for the minima down here going all the way to the maximum, and we take half of that distance, that is called the amplitude. So same thing as starting from this middle line and going to the top, or the middle line and going to the minima. So this amplitude describes the height of the wave, or we can think of it as the intensity of the wave. Another characteristic that we have to know in order to describe a wave is the frequency. And frequency is the number of cycles that pass through a point. So when we look at the number of cycles, we want to pick the same point so that we get one wavelength. So this is one wave. And we want to look at how many waves pass through a particular point within a given amount of time. And we talk about frequency in terms of cycles per second, or wavelengths per second. If you have a high frequency, you have a lot of waves passing through a given point in one second. If you have a small frequency, you have very few waves. So you can imagine very spread out kind of waves would have a lower frequency. Higher frequency would be waves that go very quickly. lower would be spread out like this. So the relationship we have between wavelength and frequency, we can see from these two examples. If we have a very short wavelength, so very small, we’re going to have a higher frequency. If we have a very long wavelength, going all the way to this one, we’re going to have a low frequency. So this is an inverse relationship. As one is larger, the other is smaller. Amplitude is not related to wavelength or frequency. So we can have a very short amplitude, we can have a very tall amplitude, and not affect either the wavelength or the frequency of a wave. So amplitude is really an intensity value. If we’re talking about light, it can indicate a brighter light or a dimmer light. If we’re talking about sound waves, it can be a louder sound or a softer sound. So it’s really just intensity. When we have a wave that represents a certain color from the visible spectrum, changing the amplitude does not change the color. We have to change the wavelength, the frequency to change the color. But we are just changing the intensity of the color if we change the amplitude. The other number that we need to know is based on the www.quicktakes.io Properties of Light Page 5/9  View this QuickTake in the app maximum speed of light Speed of light traveling through a vacuum, so no air molecules to slow it down, has been measured as 3 times 10 to the 8th meters per second. We imagine wavelength moving as a distance and frequency is the number of wavelengths per second multiplying our wavelength which I’ll say is meters times our cycles per second will give us a meters per second or a speed. So the maximum speed of light is based on wavelength times frequency. So this is where we see this inverse relationship. Since C is a constant, as wavelength goes up, frequency has to go down. If wavelength goes down, frequency has to go up. So inverse relationship. This number, speed of light, is one you will need to know. speed of light is 3 times 10 to the 8th meters per second. Knowing one or the other will help us calculate the missing one. It’s a very simple relationship. So we’re going to look at doing some calculations. When we look at light waves, it’s not simply one wave with a wavelength and a frequency and an amplitude. light travels as electromagnetic waves. Electromagnetic means we have actually two waves that are perpendicular to one another. One is 90 degrees to the other one. So you can see that in this picture. We have the electric field, which is shown as the purple line, and we have the magnetic field, which is shown as the blue. and they are 90 degrees from one another. Each of them would have a wavelength and a frequency, but they are propagating in the same direction together. So electromagnetic spectrum describes the type of light waves we see based on frequency or wavelength. So we have both descriptions on this picture. So frequency is given as this top number, and a hertz is just the same as 1 over seconds, so cycles per second. Wavelength is given down here, this is in meters, where we have different units also given in the parentheses. And remember this is an inverse relationship, so as we see frequency is higher on this end, so higher frequency down here we have lower frequency we end up having the reverse with our wavelengths alright so if we look at the spectrum there’s a few things that we recognize of course right here in the middle we have our visible region so it’s blown up in this inset down here. The visible region goes between about 400 nanometers and 700 nanometers, right in here. This is the only region where we can actually see the light waves, and we see them as different colors that are reflected back. We don’t see any of the other light waves in any of these other regions. we have the near infrared, far infrared some people use these as night vision goggles you can get some glasses or bifocals that allow you to see in the infrared lower energy than that or lower frequency than that we have microwaves and then radio waves so this end is a very low frequency which also ends up being lower energy. On the other end, we have higher frequency light waves, ultraviolet, x-rays, and gamma rays. And we think of these as having a higher energy and being able to do more damage to our bodies. So this is higher energy. Alright, so you need to know the visible spectrum is between 400 and 700 nanometers. The rest of the spectrum you don’t have to memorize at all, but we’re going to look at the relationship between the frequency and the energy for looking at where certain light waves fall on the spectrum. So our relationships then, higher energy, is a higher frequency. So frequency and energy are proportional. They are inversed to our wavelength. So over here with our higher energy, higher frequency, we have shorter wavelength. Or smaller wavelength. Over here where we have lower energy, lower frequency, we’re going to have longer wavelength. Those are inverse. At all times we have electromagnetic waves coming off of objects. Sometimes we see those as color, other times we don’t see the light waves at all. Some of what we can refer to as radiation of these electromagnetic waves. We can see this if you imagine heating something. If you heat up something on the stove or in a fireplace you can start to see the glow of some objects If you have an electric stove you can see it starts glowing red or orange when you heated up the eye Sometimes when you heated up a certain type of metal it start glowing You see this a lot of times when people are working with forges or a blacksmith who’s working with certain metals, and they heat it up, and you can start seeing that metal glowing. That’s the different electromagnetic waves coming off the object. as it’s being heated, we’re changing the energy of those waves. And we think of this as radiation. But the radiation can occur even without temperature difference. Things are radiating electromagnetic waves all the time. We just don’t necessarily see them unless they occur in the visible region. So even a cold object is radiating electromagnetic waves of some wavelength. We just don’t see it. When we start heating an object and then the electromagnetic waves move into the visible region, we start seeing it as a color. Okay, so this is described down here in this graph. This is the wavelength, and here is our visible region. Only between these wavelengths we can actually see the color. But we can see here from this graph, we always have some amount of waves coming off an object. It’s just when it’s heated to the point where it’s in the electromagnetic spectrum of the visible region, we see it as color. The sun looks yellow to us because it’s emitting radiation in that yellow region of the visible spectrum. In this picture, we can see the glowing of the metal. So he has heated up this piece of metal and now he’s hammering it into a certain shape. So this glow that looks like a color to us is because it’s emitting electromagnetic radiation in that visible region. So we see that normally when we heat objects because we’re changing the energy of the waves. so this idea of light moving as waves was explained by a lot of experimental data a lot of evidence and we could explain the electromagnetic spectrum explain the colors that we see from light moving through a prism but it didn’t explain everything and it didn’t even explain everything about light being emitted from heated objects when we started looking at it further. So if you imagine light moves as waves, very much like sound does, why is it that we can’t see through objects? Sound moving as waves can move through objects. It might be muffled or distorted, but we can still hear through walls or doors. Why isn’t that we can’t see through things? Light waves are not moving through walls or doors. When we introduce a barrier, the light moves around the barrier, but it gets stopped by the barrier. So this was the time to introduce the idea that light moves as particles. So back to Sir Isaac Newton’s idea of light being corpuscles. Max Planck described the idea of light being quantized in discrete particles light moves as particles that then vibrate at a certain frequency that looks like waves so instead of disregarding the wave idea completely we are now incorporating an idea that particles are moving like waves so instead of seeing a continuous spectrum that we would expect to see with wavelength as objects are heated when we apply the same idea to atoms when we apply an energy source to atoms sort of heating up atoms if you will and we start seeing this excitation of electrons they actually emit at very specific wavelengths. We don’t see this continuous spectrum. We see individual light bands at specific wavelengths. So that indicates that this is a quantized discrete particle and not a continuous wave. so Planck’s idea about this energy coming from light particles is described in Planck’s constant he said the energy of these photons which is what is being emitted when we excite atoms is described as energy equals Planck’s constant so Planck’s constant is this h times the frequency of the wave that the photon moves in. And since we can describe it in terms of frequency, we can also describe it in terms of wavelength using our speed of light. So both of these equations can be used depending on if you know frequency or if you know wavelength. Planck’s constant is described as 6.626 times 10 to the minus 34 joules times seconds. We can apply this to any photon from any excited atom. Alright, so we’re going to look at a few examples of calculating wavelengths and energy based on our equations. equations. So we have speed of light is equal to wavelength times frequency. We also have energy is equal to Planck’s constant times frequency, or energy is equal to www.quicktakes.io Properties of Light Page 6/9  View this QuickTake in the app Planck’s constant times c over wavelength And then our Planck constant 6 times 10 to the minus 34 joules times seconds And speed of light 3 times 10 to the 8 meters per second Alright, so what is the wavelength of light with a frequency of 3.8 times 10 to the 12th? Alright, so if we’re looking for wavelength and we’re given frequency, we’re going to use this first equation. so filling in our c speed of light, 3 times 10 to the 8th meters per second we’re looking for wavelength and our frequency 3.8 times 10 to the 12th and this is 1 over seconds alright, so you’re going to see that seconds will cancel out our wavelength will be given in meters Alright, so we’re going to divide 3 times 10 to the 8th by the 3.8 times 10 to the 12th. Alright, and I get 7.9 times 10 to the minus 5 meters. Okay, and if we want to turn that into nanometers, remember our conversion between meters and nanometers is 10 to the 9th. So this would be 7.9 times 10 to the 5th, I’m sorry, 4th nanometers. Alright, let’s look at the second one. What is the energy of a photon with this frequency? So same frequency as we had up here. So energy, we’re going to use Planck’s constant, 6.626 times 10 to the minus 34, times our frequency, 3.8 times 10 to the 12th. And our units, joules times seconds, and this frequency is 1 over seconds, so our seconds will cancel out, we’ll be left with joules, which is a unit of energy. Alright, so we’re multiplying. Alright, so I get 2.5 times 10 to the minus 21 joules. Alright, so that would be our energy. What’s the energy of a photon with a wavelength of 350 nanometers? Alright, so now we’re dealing with wavelength. So when we look at energy then, we need Planck’s constant. And we need speed of light over our wavelength. Now in this case, since the speed of light is given in meters, we have to compare units our wavelength over here is nanometers so I’m going to take the 350 nanometers and I’m going to do the conversion factor to meters so 10 to the 9th nanometers is 1 meter so all of that, so nanometers will cancel out and we’ll be left with meters so we have to make sure our units cancel So I’m going to start with 3 times 10 to the 8th and I’m going to divide it by 350 times 10 to the minus 9 and then multiply by Planck’s constant Alright, so 5.7 times 10 to the minus 19 and this is again joules because we have joules times seconds here we have meters per second and down here we have meters so our meters will cancel out here our seconds will cancel out with our Planck’s constant so we’ll be left with joules for energy Albert Einstein furthered Planck’s theory about these discrete particles by looking at what he called the photoelectric effect. If we shine ultraviolet light, which has higher energy, onto the surface of a metal, we will excite the electrons in the metal by giving them more energy, and some of those electrons will be ejected. What we see are electrons he called emitted from the surface. the energy from these we can record as different wavelengths and he called these the photons so this is the photoelectric effect introducing higher energy onto a surface exciting the electrons exciting the atoms electrons are then emitted because they have such high energy and then we see that emission as electromagnetic waves based on their energy. If we do this to atoms, we see these line spectra. And the line spectra are very predictable. So shining ultraviolet light or exciting these atoms with higher energy waves will cause the emission of electrons at specific wavelengths. and this allows us to actually identify a type of element or type of atom based on the pattern of emission that we see, sort of like a fingerprint used to identify an atom. Some examples are shown here. You can see very individual patterns being emitted. The Bohr model took advantage of this idea of individual discrete particles and quantized amount of energy that is being ejected. And Niels Bohr applied this to his Bohr model for the atom. We previously talked about the Bohr model introducing the idea of orbitals for electrons that moved around the nucleus. So Bohr incorporated these discrete energy levels to correspond with his orbitals. He said electrons within a certain orbital contain a certain amount of energy. In order to move to another orbital, they have to gain or lose energy. And they have to gain or lose a certain amount of energy in order to move to different orbitals. When they move to a lower orbital and give off energy, we see that as a photon. Alright, so this idea of quantization of energy comes from this discrete particle idea. If we imagine the staircase representing the different orbitals that an electron can be on, so orbital 1, 2, 3, 4, 5, it also represents how much energy electron needs to be in each orbital. So n1, n equals 1, being the lowest energy needed for the electron. If it wants to go up to level 2, it needs to gain a certain amount of energy in order to get to that level. To get to level 3, it needs more energy, more for 4, more for 5. okay so energy levels then are quantitized they’re not continuous like a ramp you have to go up like a stair step but not all the stairs are equal so electrons that occupy a certain orbital then have a certain energy associated okay electrons then can move between different orbitals but they have to gain or lose energy to do so. So we start numbering our orbitals at 1, 1 being closest to the nucleus, the lowest energy, and as it moves out away from the nucleus, we increase the level, the shell number, and it increases the amount of energy needed. Electrons moving then between orbitals are called electron transitions. So if I have an electron on this first energy level, and it wants to move to level 2, it’s going to have to gain energy in order to go to that next level. Electrons in what they call the ground state, which is the lowest non-excited state, can’t lose any energy. They’re in the lowest state. You have to excite them to a higher state first, and they’re called excited, and then they could fall back down to a ground state and when they do that, they emit that extra energy as a photon. Right, so here’s our example. If we have a hydrogen atom that only has one electron and that one electron in the ground state is on this first lowest energy level, it can’t lose any energy, this is as low as it gets, but it can gain energy and when it does that it’s absorbing this energy from some kind of energy source, a high energy wave, and that excites it to the second energy level. Alright, now this is an excited electron. It has absorbed energy and moved to a higher level. this excited electron now over here is then going to drop back down to the ground state when it drops back down from being an excited state to the ground state it has to release that extra energy it needed to get to level two now doesn’t need it anymore at level one so it’s going to release that energy so that light is given off, the electromagnetic wave is given off, and the electron falls back down to the first energy level. Okay, and that wave that comes off, if it has the wavelength in the visible region, we would see it as a certain color. More than likely, we wouldn’t see it at all. It’d be not in the visible region. Right, some emissions, when we see them in the visible region, come out of certain colors. So this is some examples. Moving from energy level 3 to 2 might release a certain wavelength of light. Moving from 4 to 2 would have a higher energy. Moving from 5 to 2 would have an even higher energy. So the more energy levels it’s dropping, the more energy it’s going to release, the higher energy it’s going to be, which means it’s a lower wavelength. Remember that inverse relationship. So our red is going to be higher energy. I’m sorry, our red is going to be higher wavelength, but a lower energy going into blue, purple, going into the ultraviolet would be a higher energy. We can also calculate this wavelength when electrons fall down from a higher energy level to a lower one. The Rydberg equation describes how we can calculate this wavelength. So here we have 1 over the wavelength of the light that is emitted is equal to the Rydberg constant, which we’re given up here. times, and here is our electron transition. We have 1 over the higher energy level sorry the lower energy level squared minus one over the higher energy level squared Okay so the squared value is an exponent. The one and the two represents the relationship of the energy level. So this is higher level, this is a lower level. So it can be 1 and 2, it can be 2 and 3, it can be 4 and 5, whichever energy levels it’s changing between. Alright, so we’re going to calculate the wavelength of the line spectra of hydrogen when we’re dropping down from 5 www.quicktakes.io Properties of Light Page 7/9  View this QuickTake in the app down to 2. Alright, so going back to our equation, we have 1 over the wavelength is equal to Rydberg value, 1.097 times 10 to the 7th, 1 over meters, times our difference in the reciprocal shells. So we’ll write that over here. Leave us 10, right? 7. That’s why you shouldn’t guess. Alright, 1 over meters. This one’s 2. Alright, so we’re going to do our calculation. We’re looking for wavelength. We are going from our n1 is 2 squared minus 5 squared. So that’s our equation. So I’ll do this inside the parentheses first. We have 1 over 4 minus 1 over 25. Alright, so this is 0.21. And then times our constant. So we get 2303700. zero. But this is one over wavelength, and considering inside our parentheses doesn’t have any units, we have one over meters for our unit so far, and this is one over wavelength. So this would be, if we flip this over, our wavelength would be in meters. So if I do one over this and I want to flip it in order to get wavelength. Do one divided by this and I get 4.34 times 10 to the minus 7. This would be meters. So if we’re going to do this in nanometers, we’re going to have our conversion. 10 to the 9th nanometers per meter. So multiplying by 10 to the 9th gives us 434 nanometers. Alright, so what color is this line? So 400 falls within our visible region, which is 400 to 700 is our visible region. But as we saw, this end is the red. this end over here is the violet slash blue end. So this is going to be a violet or bluish color. Here’s our energy equation again we saw with Planck’s constant. Looking at energy as equal to Planck’s constant times our frequency. So our energy is based on the frequency of the particle. so when we change the energy we are causing an excitation if it absorbs more energy we should see a higher frequency if it emits a photon it loses energy it’s going to go down relaxed to a ground state we’re going to see a lower frequency so this is our relationship between energy and frequency again Alright, so we can see here the different wavelengths emitted, and they correspond to different parts on, in this case, the visible spectra. So here’s our 434 we just saw with our calculation. It is in that kind of purplish-bluish area, the transition. The red ends up being at a higher wavelength, which is lower energy. And so when we have transitions that are only between 3 and 2, that’s less energy being lost in between 2 and 4 or 2 and 5 or 2 and 7, you know, whatever we’re going to see. For a single electron transition from one energy level to another, we can see the relationship based on that Rydberg equation. A lot of this looks very similar. But this constant value is based on hydrogen. So when we start applying this to electrons in an atom, we can really only calculate it based on what happens to hydrogen. Once you start getting more than one electron, it’s very difficult to follow the energy lost or gained from a transition. And of course, the more electrons you get, the more impossible it gets to do these calculations. So we can really only base this on hydrogen. So this number right here comes from the energy of a hydrogen transition. But we then associate this with any other transition for other atoms. So we can see the change in energy based on this number coming from hydrogen transition and then our same inverse relationship between the different energy shells squared like we saw with the Rydberg equation. Okay, so what is the energy in joules and the wavelength of the line if we see an electron moving with an n of 4 to an n of 6. So it’s going from 4 to 6. We’re increasing the energy level, so we’re going to put energy into it. So we’re going to go back and look at our equation. So negative 2.178 times 10 to the minus 18, and then we have the same parentheses we had with Rydberg. Alright, and notice this is final minus initial, so if we’re going all the way to 6, alright, that’s what we have. So I’m going to do inside the parentheses first. So 1 divided by 36 minus 1 divided by 16. Okay, this gives me a negative number, but that’s okay. We have a negative out here, so our negative is going to end up going away. So we get our change in energy, 7.59 times 10 to the minus 20. This would be joules. Alright, so there’s our change in energy that we’re going to have to put in in order to go from the 4 level to the 6 level. and then the wavelength that would be associated with this we can then apply using our equation. Energy is equal to Planck’s constant times c over wavelength. So here we have our energy. Planck’s constant speed of light over our wavelength. Alright, so I’m going to divide energy by Planck’s constant Okay, the first step, this is 1.146 times 10 to the 14 equals speed of light over our wavelength. so then moving wavelength over and dividing by that number so 3 times 10 to the 8th divided by our value gives us 2.62 times 10 to the 6 and this would be meters. Alright, so here’s our wavelength in meters. The electromagnetic spectrum, we might want to convert this to nanometers so we can get a better idea. You can also look it up in meters, but I’m just going to convert it to nanometers so we can see if it’s in the visible region or not. And this is not. nanometers? Ah, nanometers. Alright, so this is greater than our visible region. So visible region was 400 to 700. This is greater than that. So we have a longer wavelength, which means it’s going to be lower energy. Going from 4 to 6 is actually not a big energy jump, because as you get Further away from the nucleus, the energy needed to go between the different levels actually gets less and less. So our Bohr model looks at the quantized energy level. Electrons move in orbitals. Each orbital has a certain energy associated with it. Electrons can move between different orbitals, but they have to do so by gaining or releasing energy. the electron becomes more tightly bound its energy becomes more negative relative to the reference or the free electron. As the electron gets closer and closer to zero energy it gets further from the nucleus until it’s no longer bound at all to the nucleus. So exciting the electron has it moving further and further from the nucleus until it’s considered free and no longer bound to the nucleus moving in orbitals around it. de Broglie determined that waves are actually more common than we think. So light moves as waves, light moves as particles, but in reality everything actually moves as waves. There is a wave functionality to all matter regardless of the mass, but it an inverse relationship as the mass of an object gets larger and larger its wavelength gets smaller and smaller so that we don see the actual movement as a wave any longer We can see electrons or photons moving as waves because their mass is so tiny. But as the mass of things get larger and larger, their wavelengths get smaller and smaller and no longer looks like it’s moving as a wave. So de Broglie’s ideas is called the wave properties of matter. And it applies to all matter, but most people apply it to electrons because we can actually see the wavelength. So it says the wavelength is equal to Planck’s constant divided by the mass of the particle times its velocity. Okay, so if we look at this written in this way, mass and velocity are on the bottom part of the fraction. Alright, so as the mass gets very large, imagine the bottom part of this ratio getting very, very large, the wavelength gets very, very small. For a very small mass, we get a much larger wavelength. So that’s that inverse relationship. Electrons being so small, and this is our mass of an electron, we can actually get a larger wavelength where we can see it moving as a wave. But really, everything moves as waves. Baseballs, airplanes, tennis balls, everything moves with wavelike properties, but their wavelengths are so small. and remember small wavelength means very high frequency it’s essentially moving so much like this that it starts to look like a straight line even though it’s a wave with just really really tiny wavelengths so the larger something is the smaller the wavelengths so we don’t see its wave- like motion so if we think about a baseball being thrown at 44 meters per second, or 98 miles per hour. Diameter of the ball is 15 centimeters. What do we see about the size of the wavelength? Alright, so our wavelength is equal to Planck’s constant over mass times velocity. So if we solve for the wavelength of this, okay, so this is joules times seconds for our Planck’s constant, Our mass has to be in kilograms. Okay, and then our velocity is meters per second. So that’s 44 meters per second. We can calculate the wavelength. So 6.626 times 10 to the minus 34. and we’re going to divide by 0.142 kilograms and divide by 44 meters per second www.quicktakes.io Properties of Light Page 8/9  View this QuickTake in the app so our wavelength is 1.06 times 10 to the minus 34 and this is meters. So very, very, very tiny wavelength so much so that we don’t see it moving as a wave. So the last idea that has to do with observing these electrons and where they are and how they move and how fast they move has to do with how we can see the electrons. Electrons are moving in these orbitals, but we can’t look at electrons. We can’t use a microscope to see the electrons moving. Electrons are so small that in order for us to see something, we have to have reflected light come off the object. So light hits an object, is reflected back, and we see it with our eye, based on that wavelength. In order to have light reflected off an electron that is so tiny, we would have to have a wavelength with a very high frequency. Okay, to make sure the light wave could hit the electron and didn’t just miss it because its wavelength was too big. So very small wavelength, very high frequency. But light waves with very high frequency have very high energy. So if we hit an electron with a wavelength with very high energy, it’s going to cause it to move. Right? If we hit an electron with high energy, it moves to a higher energy level or gets ejected off the atom completely. So to observe an electron, we would have to disturb its course and position, because we would be hitting it with a very high energy wave. So we can’t do that, which leads to Heisenberg’s uncertainty principle. You can’t observe something without changing its course and position. Okay, so the uncertainty is we can never know exactly both the position of electron and the momentum of the electron at the same time. Because by observing it, we are changing it. And people have applied Heisenberg’s uncertainty principle to other concepts as well with the same idea. How you see something depends on how you choose to observe it. and the action of observing something normally alters it. So the Heisenberg uncertainty principle is given as this, which says the uncertainty of position, so x is the position of something, so change in position times uncertainty of momentum, so this p is momentum, change in position times change in momentum is greater than Planck’s constant over 4 pi. So the uncertainty is always greater than the certainty of knowing where it is. So you can observe an electron as a particle, as a wave, based on the experimental data we’ve already seen so far, but you can’t observe it as both at the same time. We can’t know where it is and know how it’s… www.quicktakes.io Properties of Light Page 9/9