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### Course: AP®︎/College Physics 2 > Unit 7

Lesson 1: Wave-particle duality# Photon energy

Learn what a photon is and how to determine the energy of a photon as you explore the dual nature of light as both a wave and a particle, known as wave-particle duality. Uncover the concept of quantum mechanics, where light deposits energy in discrete amounts called photons. Investigate Planck's constant and how it relates to the energy of a photon. Created by David SantoPietro.

## Want to join the conversation?

- Photons are light particles because they exhibit particle like behavior. But are they actual/physical particles?(92 votes)
- Wave particle duality could better be understood by the fact that all particles on a quantum level are described by wave functions in order to describe their location, which we can't exactly know due to the Heisenberg Uncertainty Principle. Because of the uncertainty, we must describe particles as a function of it's likely locations, so thusly the particles act like waves because we don't know their exact position and must describe them as waves. This is why we can see wave particle duality with things as large as bucky balls(60 Carbon atoms) in experiments such as the double slit experiment. To summarize, photons ARE particles that just show wave behaviour due to us having to describe them as wave functions due to uncertainty of their position. At least this is what I gather after reading QED from Feynman, but I won't pretend to understand anything (Neither did Feynman.)(28 votes)

- At5:00David mentions Planck discovering this smallest, discrete amount of energy that light can deliver (6.626 x 10^-34 (J·s)). My question: how did Planck, in 1900 (!), quantify such a small quantity of energy?(41 votes)
- He calculated it by making the hypothesis that energy comes only in discrete packets (i.e. the photon). He uses this assumption to calculate the frequency distribution of black body radiation with his constant h being the separation between allowed frequency values and it exactly matched what was experimentally observed.(42 votes)

- Just out of curiosity.

Light travels at different speeds in different medium.

Can't we use medium that has extremely high n value to slow speed of light to a level that we can capture, photograph light photons and examine its properties little better?(40 votes)- Scientists have photographed light moving, so yes with a trillion frames a second you can photograph light moving through a bottle https://www.ted.com/talks/ramesh_raskar_a_camera_that_takes_one_trillion_frames_per_second?language=en(25 votes)

- 'Energy cannot be created or destroyed' then where did all the initial energy in the big bang come from?(16 votes)
- The big bang created an equal amount of positive and negative energy and mass, so if you were to calculate the mass and energy of the universe, you find that it actually equals 0, so no law is broken.(5 votes)

- Can you give an example problem for E=hf?(5 votes)
- Calculate the wavelength of a photon emitted when an electron in a hydrogen atom undergoes a transition from n = 2 to n = 1.(15 votes)

- At4:57, is frequency a measure of the wave (of light) frequency? If so, how does it fit with the idea that light is a particle? How is a particle supposed to have a frequency?(7 votes)
- Yes, frequency is a measure of the wave of light. This is ok with the understanding that light is a particle because all particles do have frequency. All of the particles in your body technically have wave like properties (frequency and wavelength). Check out the De Brogli wavelength: http://calistry.org/calculate/deBroglieEquation

Ordinary particles have a wavelength so small that we can't see the oscillations (this is because ordinary particles have mass). Photons, on the other hand, do not have mass. Their nonexistent mass and high speed (speed of light, c) cancel out nicely to produce noticeable wave like behavior.(7 votes)

- Why is that Photons are known to be mass less? But at the same time it has MOMENTUM? Then how can it physically interact with matter?(6 votes)
- Photon is the quantum of light and light is electromagnetic wave which carries momentum and energy.

i.e, If the total energy transferred to a surface in time t is U, then p=U/c . So there, is interaction of photon with matter. Take an example you can see the surrounding because photons interact with matter.(4 votes)

- There has been something that has been bothering me ever since I entered the realm of physics and chemistry, it's that how are constants discovered? In school, they just give us the constants as a given and we have to memorize it, but it always nags me that I don't know how it was found out in the first place.(7 votes)
- Most constants are measured. For example when you look at the ideal gas law PV=nRT the constant R is determined by measuring the pressure and volume and then measuring the number of molecules and the temperature and put them in the rearranged equation R=(PV)/(nT).(2 votes)

- When he completes the equation of E = hf, the seconds and the Hz just disappear and he is left with only J. How do seconds and Hz cancel each other out? I thought Hz was equal to seconds^-1, but am I wrong? Can someone explain how this works?(4 votes)
- Hz is seconds^(-1): seconds*(1/seconds)=1 just like 5*(1/5)=1(4 votes)

- what if you fuse photons and dark matter together(2 votes)
- Dark matter is called that because it doesn't interact via the electromagnetic force so photons will not interact with dark matter.(3 votes)

## Video transcript

- We've been treating light as a wave, and we've been drawing it with
this continuous wave pattern of oscillating electric
and magnetic fields that are traveling in some direction. And why shouldn't we treat it as a wave? If you sent it through a small opening, this electromagnetic
radiation would spread out, There'd be diffraction,
and that's what waves do. Or, if you let it overlap with itself, if you had some wave in some region, and it lined up perfectly with some other electromagnetic wave, you'd get constructive interference. If it was out of phase, you'd
get destructive interference. That's what waves do. Why shouldn't we call
electromagnetic radiation a wave? And that's what everyone thought. But, in the late 1800s and early 1900s, physicists discovered something shocking. They discovered that light, and all electromagnetic radiation, can display particle-like behavior, too. And I don't just mean localized
in some region of space. Waves can get localized. If you sent in some wave
here that was a wave pulse, well, that wave pulse is
pretty much localized. When it's traveling
through here, it's going to kind of look like a particle. That's not really what we mean. We mean something more dramatic. We mean that light, what
physicists discovered, is that light and light particles can only deposit certain amount of energy, only discrete amounts of energy. There's a certain chunk of
energy that light can deposit, no less than that. So this is why it's
called quantum mechanics. You've heard of a quantum leap. Quantum mechanics means a
discrete jump, no less than that. And so what do we call
these particles of light? We call them photons. How do we draw them? That's a little trickier. We know now light can behave
like a wave and a particle, so we kind of split the
difference sometimes. Sometimes you'll see it like this, where it's kind of like a wavy particle. So there's a photon,
here's another photon. Basically, this is the problem. This is the main problem
with wave particle duality, it's called. The fact that light, and
everything else, for that matter, can behave in a way that shows
wavelike characteristics, it can show particle-like characteristics, there's no classical analog of this. We can't envision in our minds
anything that we've ever seen that can do this, that can
both behave like a wave and a particle. So it's impossible, basically, to draw some sort of
visual representation, but, you know, it's always
good to draw something. So we draw our photons like this. And so, what I'm really saying here is, if you had a detector sitting over here that could measure the light
energy that it receives from some source of
light, what I'm saying is, if that detector was sensitive enough, you'd either get no
light energy or one jump, or no light energy or, whoop,
you absorbed another photon. You couldn't get in between. If the quantum jump was
three units of energy ... I don't want to give you a
specific unit yet, but, say, three units of energy you could absorb, if that was the amount of
energy for that photon, if these photons were carrying
three units of energy, you could either absorb
no energy whatsoever or you could absorb all three. You can't absorb half of it. You can't absorb one unit of
energy or two units of energy. You could either absorb
the whole thing or nothing. That's why it's quantum mechanics. You get this discrete behavior of light depositing all its energy
in a particle-like way, or nothing at all. How much energy? Well, we've got a formula for that. The amount of energy in one photon is determined by this formula. And the first thing in
it is Planck's constant. H is the letter we use
for Planck's constant, and times f. This is it. It's a simple formula. F is the frequency. What is Planck's constant? Well, Planck was basically the
father of quantum mechanics. Planck was the first one to figure out what this constant was and to propose that light can only deposit
its energy in discrete amounts. So Planck's constant is
extremely small; it's 6.626 times 10 to the negative
34th joule times seconds. 10 to the negative 34th? There aren't many other
numbers in physics that small. Times the frequency --
this is regular frequency. So frequency, number of
oscillations per second, measured in hertz. So now we can try to figure out, why did physicists never
discover this before? And the reason is, Planck's
constant is so small that the energy of these
photons are extremely small. The graininess of this
discrete amount of energy that's getting deposited is so small that it just looks smooth. You can't tell that
there's a smallest amount, or at least it's very hard to tell. So instead of just saying 'three units,' let's get specific. For violet light, what's the
energy of one violet photon? Well, the frequency of violet light is 7.5 times 10 to the 14th hertz. So if you take that number
times this Planck's constant, 6.626 times 10 to the negative 34th, you'll get that the energy
of one violet photon is about five times 10 to
the negative 19th joules. Five times ten to the negative 19th, that's extremely small. That's hard to see. That's hard to notice, that energy's coming in
this discrete amount. It's like water. I mean, water from your sink. Water flowing out of your
sink looks continuous. We know there's really discrete
water molecules in there, and that you can only
get one water molecule, no water molecules, 10 water molecules, discrete amounts of these water molecules, but there's so many of
them and they're so small, it's hard to tell that it's
not just completely continuous. The same is happening with this light. This energy's extremely small. Each violet photon has an
extremely small amount of energy that it contributes. In fact, if you wanted
to know how small it is, a baseball, a professional
baseball player, throwing a ball fast, you know, it's about 100 joules of energy. If you wanted to know how
many of these photons, how many of these violet
photons would it take to equal the energy of one baseball thrown at major league speed? It would take about two million trillion of these photons to equal the energy in a baseball that's thrown. That's why we don't see
this on a macroscopic scale. For all intents and
purposes, for all we care, at a macroscopic level,
light's basically continuous. It can deposit any energy whatsoever, because the scale's so small here. But if you look at it up close, light can only deposit discrete amounts. Now, I don't mean that
light can only deposit small amounts. Light can deposit an
enormous amount of energy, but it does so in chunks. So think about it this way ... Let's get rid of all this. Think about it this way: let's say you had a detector
that's going to register how much energy it's absorbing, and we'll graph it. We'll graph what this
detector's going to measure, the amount of energy per
time that it measures. So we'll get the amount
of energy per time. Now, you can absorb
huge amounts of energy. And on the detector,
on a macroscopic scale, it just might look like this. You know, you're getting
more and more light energy. You're absorbing more and more energy, collecting more and more energy. But what I'm saying is
that, microscopically, if you look at this, what's happening is, you've
absorbed one photon here. You absorbed another one, absorbed another one, absorbed a bunch of them. You keep absorbing a
bunch of these photons. You can build up a bunch of energy. That's fine. It's just if you looked
at it close enough, you have this step pattern that's absorbing photons at a time, certain numbers of them. Maybe it absorbs three at one moment, four at another moment. But you can't absorb anything in between. It can't be completely continuous. It has to be a discrete
all-or-nothing moment of absorption of energy
that, on a macroscopic scale, looks smooth but on a
microscopic scale is highlighted by the fact that light energy
is coming in discrete chunks, described by this equation that gives you the energy of
individual photons of light.