mpton found that this relationship hold instead
24:03 the wavelength of scattered light minus the initial wavelength of the light
24:07 equals Planck's constant divided by the product at the speed of light
24:11 and the massive whatever the light was striking which in this case was an
24:15 electron
24:15 times one minus cosign a fee were he is the angle at which the light was
24:20 deflected
24:21 obviously the incoming and outgoing wave lengths are not equal
24:25 if they were there difference would be zero instead
24:29 this equation implies that the wavelengths have scattered light are
24:32 larger than the wavelength of the incoming light
24:34 and once again we have this mysterious factory H in the equation
24:39 so what's going on here the situation is analogous to what happens in a game of
24:44 pool
24:44 when a billiard ball strikes the side of the pool table
24:47 a transfer some others energy to the wall causing it to require oil well the
24:51 billiard ball rolls off in some direction
24:54 similarly when light scatters of an electron
24:57 it strikes it with a certain amount of energy which causes the electron trick
25:01 while
25:01 and the light then bounces away somewhere else with less energy since it
25:04 already transferred some to the electron
25:06 now this is all well and good but can't
25:09 equation doesn't tell us anything about the energies and light beams
25:13 well actually it does if you accept the particle picture a flight
25:16 which ties everything together quite nicely the wavelength
25:20 any electromagnetic wave is proportional to its frequency
25:24 if we accept that this light is comprised of photons
25:27 then using the Planck unstained relation we can show that since a change in
25:31 wavelength corresponds to a change in frequency
25:33 and since the change in frequency corresponds to a change in energy
25:37 that a change in wavelength must correspond to a change in energy
25:40 why does that matter because Commons aqui Asian tells us something very
25:45 important
25:45 about how the motion of a photon corresponds to how much it's energy
25:49 changes
25:50 if we're dealing with a situation where photons are just hitting electrons
25:55 what you have here are a bunch of constant terms multiplied by this
25:58 parameter
25:59 which is what determines how much a boat owns wavelength and by extension how
26:03 much are protons energy
26:04 changes when it scatters what we find is that the change in energy depends on the
26:09 angle
26:10 at which the photon scatters if the angle is zero
26:13 that is it the photon just passes through without scattering of have
26:16 anything
26:17 the change in the photons wavelength 0 which seems pretty reasonable
26:21 if it doesn't scatter offered anything its energy is not gonna change so the
26:25 wavelengths not gonna change
26:27 if the photon scatters of an electron at an angle of 90 degrees however
26:31 the change in its wavelength will be equal to these constant terms times one
26:35 and if the vote on scatters of an electron at an angle about 180 degrees
26:40 that is it hits the electron directly and moves back exactly the way it came
26:44 the change in wavelength will be twice as high in other words the more directly
26:49 hit
26:49 the greater the change in wavelength and by extension the greater the change in
26:53 energy
26:54 from the standpoint of particles like billiard balls
26:58 this makes perfect sense a head on collision is going to transfer more
27:01 energy than a glancing blow
27:03 from all others Compton was able to show that light must behave like a particle
27:08 in order for these results to make sense
27:10 by painting such a beautiful picture of how the photon theory a flight must be
27:14 correct
27:15 Compton had confirmed I'm Stansbury beyond any reasonable doubt
27:19 any got a Nobel Prize for it so at last we had this picture a flight breaking
27:24 behave like a particle when it's omitted
27:26 they can behave like a particle when it bounces off of things and it behaves
27:29 like a particle when it gets absorbed
27:31 but physicists were not very happy with this since there was equally
27:35 overwhelming evidence that light was a wave
27:38 interference diffraction and dispersion were
27:41 indisputable but these properties are exclusively wave-like
27:45 particle simply don't have any property is that would allow them to do these
27:49 things
27:50 waves and particles are incompatible
27:53 their properties are mutually contradictory and completely
27:56 irreconcilable
27:57 and yet by c