The Photon

Transcript

0:00Introduction

Hello everyone! Let me start with a small puzzle. When you jump off a small boat onto the shore, the boat moves backwards, right? Now, a sodium atom at rest gives out a single flash of light. Does the atom also move backwards? Can light really push something? Example two will answer that. Photon questions come up often in JEE, so let's begin.

0:24Light comes in packets: the photon

So, here is the big idea. When radiation interacts with matter, it behaves as if it were made of particles, and we call these particles photons. Little packets of light, okay? Now, how much energy does each photon carry? Capital E equals h times nu. Here nu, the Greek letter that looks like a v, is the frequency, and h is the Planck constant. We can also write it as h c over lambda, where c is the speed of light, and lambda, the Greek letter at the bottom, is the wavelength. Right? And h is six point six three times ten to the power minus thirty four, in joule seconds. The cross means times, the small raised number is the power of ten, and the J and the small s stand for joule second. Clear? Now let me ask you something. Take one photon of red light and one photon of blue light. Which one carries more energy? Very good, it is the blue photon! Blue light has the higher frequency, so h nu is bigger. So a red-light photon has less energy than a blue-light photon. With me?

1:35Photons carry momentum too

Now, a particle carries momentum, and so does a photon. Small p, the momentum, equals h nu over c, which is h over lambda, which is also capital E over c. Pick whichever form fits the data. Okay? Next, photons travel at the speed c in vacuum, and they have zero rest mass. Zero rest mass, and still they carry momentum! Right? So let me ask you this. Can a magnetic field bend the path of a photon? No, it cannot, and the reason is simple. Photons are electrically neutral; they have no charge. So neither electric nor magnetic fields can deflect them. Got it? And in a collision between a photon and a particle, total energy and total momentum are conserved. But the number of photons need not be! Sometimes a photon is absorbed, and sometimes a new one is created.

2:30Brighter light: more photons, not stronger ones

Clear? Now, a quick question, and be honest. Take a beam of light, and make it ten times brighter. So each photon now carries ten times the energy, right? Oh no, careful, that is a classic JEE trap, and many students fall into it. All photons of a given frequency have the same energy and the same momentum, whatever the intensity. The double arrow means implies. You did not change the frequency, so nothing changes for each photon. Okay? So what does a brighter beam really have? More photons, not more energetic ones. You will need this line again when we study electron emission. With me? One more question. Light goes from air into glass, and its wavelength changes. So, does the energy of each photon change as well? No, it does not, and here is why. When light enters a medium, its frequency, nu, does not change. So the energy of each photon, h nu, stays exactly the same. Clear?

3:35Topper's shortcut: work in electron volts

Now, photon energies in joules are awkward, with all those powers of ten. So we use the electron volt, written as small e and capital V on screen. One electron volt equals one point six times ten to the power minus nineteen joule. Okay? And here is a number worth memorising. h times c equals one thousand two hundred and forty, in electron volt nanometres. The n m on screen is the nanometre. Right? So here is the topper's shortcut. The energy in electron volts equals one thousand two hundred and forty over the wavelength in nanometres. The brackets just remind you of the units. And the trap? Put the wavelength in metres, and the answer is nonsense. So nanometres only, got it?

4:24Example 1: photon energy in joules and eV from its frequency

Alright, example one, an easy one. Find the energy of a photon of frequency six point zero times ten to the power fourteen hertz, in joules and in electron volts. Hertz, written capital H and small z, means per second. Pause the video and try it first. Done? Okay, let's check. Capital E equals h nu, so it is six point six three times ten to the power minus thirty four, times six point zero times ten to the power fourteen. Okay? Now multiply. Six point six three times six gives thirty nine point seven eight. For the powers, minus thirty four plus fourteen gives minus twenty. So that is thirty nine point seven eight times ten to the power minus twenty joule, about three point nine eight times ten to the power minus nineteen joule. The wavy equals sign means approximately. Right? Now change it to electron volts. Do we multiply by one point six times ten to the power minus nineteen, or do we divide? We divide, yes, exactly, since each electron volt is one point six times ten to the power minus nineteen joule. Three point nine eight over one point six gives two point four nine, and the powers of ten cancel. So the photon has about two point four nine electron volts. Much friendlier, isn't it?

5:53Example 2: recoil speed of a sodium atom emitting a photon

Now example two, our puzzle from the start. One sodium atom, of mass three point eight two times ten to the power minus twenty six kilogram, is at rest. It emits a photon of wavelength five hundred and eighty nine nanometres. Find the speed of recoil, the speed with which the atom moves back. Pause the video and try it first. Done? Okay, let's check. Before the emission, the atom is at rest, so the total momentum is zero. Now tell me, after the photon flies off, what must the total momentum be? Still zero, yes, exactly, because momentum is conserved! So the atom must move the opposite way, with momentum equal in size to the photon's. That gives m times v equals h over lambda, where m is the mass of the atom and v is its speed. Clear? Now put in the numbers. So v equals six point six three times ten to the power minus thirty four, over the mass times the wavelength. Watch the units: five hundred and eighty nine nanometres is five point eight nine times ten to the power minus seven metre. Forget that change, and the answer is way off. Okay? Now the bottom of the fraction. Three point eight two times five point eight nine gives about twenty two point five, so the bottom is about two point two five times ten to the power minus thirty two. Six point six three over two point two five gives about two point nine, and the powers leave ten to the power minus two. The m and the s with the raised minus one mean metres per second. With me? That is two point nine centimetres per second. So yes, the photon carries momentum, and the atom really is pushed back! Just like the boat when you jump off it, the atom moves back as its photon flies away. Small, but completely real. Got it?

7:54Quick revision: E = hc/lambda, p = h/lambda, 1240 shortcut

So, quick revision. Each photon carries energy h nu, which is h c over lambda, and momentum h over lambda, which is capital E over c. Then, a brighter beam has more photons, with the same energy each. And the energy in electron volts is one thousand two hundred and forty over the wavelength in nanometres. Now go and try the practice problems on this page. All the best!