0:02 the topic of this video is development
0:03 of quantum theory behavior in the
0:05 microscopic world
0:06 the learning objective for this video is
0:08 on your screen
0:12 the physicist louis
0:18 wanted to know if electromagnetic radiation
0:19 radiation
0:21 which we classically thought of as a wave
0:22 wave
0:24 could at times depending on the
0:26 measurement and the context
0:28 have particle-like properties which the
0:30 particle being a photon
0:33 in the photoelectric effect for example if
0:33 if
0:36 if if that happens for electromagnetic
0:38 radiation what about for matter
0:40 what if matter which we thought of
0:42 classically as having particle like
0:45 uh properties could at times depending
0:47 on the context
0:50 and experiment have wave-like properties
0:58 particles have
1:01 wave like properties
1:08 so if if a particle such as an electron
1:09 does have wave-like properties
1:11 here's how we could think about it
1:12 instead of a particle
1:16 orbiting around a nucleus
1:19 at a fixed energy state you know the
1:20 ground state or it could be excited up to
1:21 to
1:24 an excited state but instead of a particle
1:25 particle
1:28 orbiting around the nucleus
1:31 instead there'd be a standing wave okay
1:32 so it's no longer a particle but actually
1:33 actually
1:37 uh the electron is a standing wave
1:40 and we can define a wavelength here so
1:42 this is what we refer to as
1:44 the debris wavelength and there's some
1:46 average distance from the nucleus which
1:47 would be the
1:50 radius here okay so what do i mean by
1:53 the debris wavelength well this is um
2:03 and it's a mathematical expression
2:05 where we have lambda which is the roy wavelength
2:06 wavelength
2:09 is equal to planck's constant over mass
2:12 times velocity so this is a v here it's
2:14 not we're not talking about frequency
2:17 um and uh
2:22 so here this is the de bruy wavelength
2:49 radiation um and so
2:52 again here m is mass v
2:58 and something important here is that we
2:59 can still
3:02 use aspects of the bohr model where
3:04 there are discrete energy states
3:04 available to
3:06 an electron except now we don't have to
3:08 think about it as a particle we can
3:10 think about the electron as a standing wave
3:10 wave
3:14 that whose radius can expand from
3:17 the center of uh of the atom or the nucleus
3:18 nucleus
3:21 so a mathematical expression here is
3:24 2 pi r r being the radius up above
3:28 is equal to n some integer n
3:32 multiplied by the derivative wavelength
3:35 and here n is equal to
3:39 1 2 3 or pretty much any
3:43 integer positive integer up to infinity
3:45 so you could see here that at a fixed
3:48 debris wavelength
3:50 all we have to do is increase this
3:51 integer value
3:53 n and that would predict we would
3:55 predict that
3:57 we would have a higher or a larger
4:00 radius of the standing wave okay so this
4:02 is reminiscent of of the bohr
4:06 model um okay so
4:08 if the prediction if that was the big
4:10 question then is there any evidence that
4:11 electrons do
4:13 have wave-like properties so this was tested
4:14 tested
4:19 by using a double slit style experiment
4:22 and again a double slit is one in which
4:24 waves passing through a double slit
4:26 will constructively and destructively
4:28 interfere on the other side of the slit
4:29 over in this region here that i'm
4:30 circling in red
4:34 and any detector here will pick up that
4:35 constructive interference where the waves
4:37 waves
4:39 added up to each other to produce a
4:41 higher signal and then the dark regions
4:42 here where there is destructive
4:44 interference where the waves
4:47 um uh cancel each other out
4:50 and so this wave pattern is definitely
4:51 or this interference pattern
4:54 uh is reminiscent of of of
4:57 wave-like behavior now if you
4:59 in the this experiment they took an
5:01 electron source and
5:03 they thought you know okay these are
5:05 particles that were blasting
5:08 um at this double slit but what they
5:10 ended up observing in detectors is that
5:12 if you let enough
5:15 time pass and you collect enough data here
5:15 here
5:17 what you'll see is an interference
5:19 pattern will eventually emerge and this
5:20 interference pattern
5:29 here we can say electrons do
5:34 have wave like
5:38 properties so this is this is a huge
5:40 you know uh development because now we
5:42 think electrons
5:45 don't have to be uh this particle
5:47 orbiting around a nucleus so atoms
5:49 aren't we don't have to think about them
5:51 as little solar systems of particles
5:52 zipping around
5:54 but instead for the electron we can
6:03 in the atom so now what i want to do
6:06 is go to a practice problem
6:09 where we can use the equation that i
6:10 showed above for the debris wavelength
6:13 so so here we can actually calculate the
6:14 the the wavelength
6:16 of a soft ball okay so this is a
6:18 macroscopic object
6:20 with a mass of 100 grams traveling at a
6:22 velocity of 35 meters per second
6:23 okay so we're making the assumption it
6:26 can be modeled as a single particle
6:29 so let's go ahead and do this um the
6:30 equation from above is the debris
6:32 wavelength is equal to planck's constant over
6:33 over
6:36 mass times velocity uh before i
6:42 planck's constant here i want to point
6:44 out to you that
6:46 planck's constant units are joules times seconds
6:47 seconds
6:49 but in this problem we have a mass on
6:50 the denominator of
6:53 and it's given to us in grams um and we
6:54 also have a velocity so meters and
6:56 seconds so there's no way that these units
6:56 units
7:00 can can be canceled as is but
7:04 a joule is also is equivalent to the
7:06 following units and it's kind of bizarre
7:09 kilogram meters squared per second squared
7:10 squared
7:13 that uh whole
7:15 ensemble of units kilograms times meter
7:16 squared divided by second squared is
7:18 actually equivalent to one joule
7:21 so i'm actually going to switch and use
7:25 um that in place of joules and so i'm
7:26 but i still have to tack on the seconds
7:27 here because that's also part of
7:29 planck's constant
7:31 okay so we're not going to use this
7:33 anymore we are going to use
7:34 this version over here but we can
7:36 simplify it a bit seconds here will
7:38 cancel out with the second squared on
7:39 the bottom
7:41 so when i write out planck's constant
7:42 over here
7:46 6.626 times 10 to the negative 34th
7:49 all i'm going to write is kilogram times
7:50 meter squared
7:53 times reciprocal seconds one over seconds
7:55 seconds
7:57 now this will make the units uh easier
7:59 to to cancel out
8:00 uh but we still have something else to
8:02 consider so the mass is 100 grams but
8:04 we have grams in the denominator
8:06 kilograms in the numerator so we need a
8:08 unit conversion here
8:10 so we know that there are 1000 grams per
8:12 one kilogram
8:15 and then the velocity units are fine uh
8:16 they are meter
8:19 per second so what we'll do here is uh
8:20 check that all of our units will cancel
8:22 we have kilograms we'll cancel kilograms
8:25 grams with grams meters with the meters
8:27 squared here
8:29 and reciprocal seconds with reciprocal
8:30 seconds so we'll be left with
8:34 units of meters which is exactly what we
8:35 would expect for
8:38 a wavelength and this should give you a
8:39 value of
8:43 1.9 times 10 to the negative 34
8:46 meters and so the the key
8:48 point here is we can calculate a
8:50 wavelength for a softball but
8:52 but the magnitude is so small that it
8:53 has no real
8:56 perceptible effect in the macroscopic
9:00 uh domain okay so there's no real
9:03 uh way to test whether a softball
9:05 has this wavelength it's so small but if
9:07 you have a really really really small
9:10 piece of matter such as an electron
9:11 and you calculate the debris wavelength
9:13 of that electron you'll find that it
9:14 actually has
9:17 a a wavelength that is larger
9:20 than the size of the particle itself and so
9:21 so
9:24 then in the macroscopic domain the
9:27 wave-like characteristics of matter become
9:28 become
9:34 one final thing here is the heisenberg
9:36 uncertainty principle
9:40 and this will come up when you take
9:43 a future chemistry class on quantum chemistry
9:44 chemistry
9:48 but here it is worth pointing out um
9:51 that it is fundamentally
9:55 impossible to determine
9:59 simultaneously and exactly
10:02 both the momentum
10:07 and the position of a particle
10:10 so what does that mean it means that
10:13 uh if particles have wave-like behaviors
10:14 there is some limit
10:17 into how well we can measure certain
10:18 properties of
10:23 of these particles and so briefly
10:25 what we can say here is that delta x is
10:27 the uncertainty
10:31 in a particle's position
10:34 and this will be um in the other unit
10:36 here this will be mass times the change
10:37 in velocity so this is
10:41 a change in momentum okay uh
10:43 the both of these multiplied by each
10:44 other are always
10:46 greater than or equal to this constant
10:48 planck's constant over
10:51 4 pi so what that means is
10:54 if your uncertainty
10:58 in the position of a particle goes
11:01 down so you become more certain of where
11:02 that particle is
11:06 you become less certain of its
11:10 momentum on the right and vice versa
11:12 so this is essentially the basis of the
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