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- [Voiceover] If you
didn't watch the last video

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because there was too much physics,

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I'll just quickly summarize
what we talked about.

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We went over the Bohr
model of the hydrogen atom,

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which has one proton in its nucleus,

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so here's the positive
charge in the nucleus,

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and a negatively charged
electron orbiting the nucleus.

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And even though this is not reality,

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the Bohr model is not
exactly what's happening,

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it is a useful model to think about.

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And so we just assumed the electron

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was going in this direction

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So counter-clockwise around
which gives our electron

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a velocity tangent to our circle,

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which we said was v in the last video.

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And in the last video, we
calculated this radius.

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So we calculated the
radius of this circle,

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and we said this was equal to r one.

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So r one turned out to be five
point three times 10 to the

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negative eleventh meters,
which is an important number.

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And we also derived this equation, right.

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So r for any integer n is
equal to n squared times r one,

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for example, if you wanted
to calculate r one again.

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So the first allowed
radius using the Bohr model

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is equal to one squared times r one.

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And so obviously one squared
is one so r one is equal to

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five point three times 10 to
the negative eleven meters.

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And so when n is equal to one,

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we said this was an electron
in the ground state,

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in the lowest energy state for hydrogen.

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We'll talk about energy
states in the next two videos.

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So this is a very important number here.

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So this is, this number right here,

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is the radius of the smallest
orbit in the Bohr model.

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In the previous video, we
also calculated the velocity

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or we came up with an
equation that you could use

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to calculate the velocity
of that electron.

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If you go back to the previous video,

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you'll see the equation that
we derived was the velocity is

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equal to the integer n
times Planck's constant

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divided by two pi m times r,

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and we figured this out
using Bohr's assumption

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for quantised angular momentum

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and the classical idea
of angular momentum.

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So if we plug in some numbers here,

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we can actually solve for
the velocity of this electron

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cause we're gonna take
this radius and we're gonna

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plug it in down here and then we know what

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these other numbers are.

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So we said n was equal to
one, so we're talking about

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n is equal to one so we're
going to plug a one to here.

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So this will be a one.

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The velocity is equal to
one times Planck's constant,

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six point six two six
times 10 to the negative 34

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divided by two pi times m.

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And we're talking about
the electron so m was the

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mass of our electron, which
is nine point one one times

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10 to the negative 31st kilograms.

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And finally, for n is
equal to one, this was our

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allowed radius so we can
plug this in for our radius,

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five point three times
10 to the negative 11.

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So if you do all that
math, I won't take the time

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to do it here, but you'll get a velocity

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approximately equal to,
approximate sign, two point two

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times 10 to the sixth and
your units should work out

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to meters per second
so that's the velocity.

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So going by the Bohr
model, you can calculate

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the radius of this circle
here so you can calculate

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this radius, and you can
also calculate the velocity.

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And,again, this isn't
reality but we'll use these

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numbers in later videos so
it's important to figure out

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where they came from.

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So this is the radius of
the smallest orbit allowed

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using the Bohr model but
you can have other radii,

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and we can calculate the
radii of larger orbits

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using this equation.

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So we're just gonna use
different values for n.

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So we started off with n is equal to one.

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Let's use the same equation and let's do

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n is equal to two.

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So let me go ahead and rewrite
that equation down here.

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Let's get some room.

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So r for any integer n is
equal to n squared times r one.

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Let's do n is equal to two here.

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So n is equal to two so let's
go ahead and plug in two.

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So we'd have two squared times r one.

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So r two, the second
allowed radii or the second

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allowed radius I should say,
is equal to four times r one.

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So if we're thinking about a picture,

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let's say this is the nucleus here

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and then this tiny, little
radius here is r one.

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If we wanted to sketch in
the second allowed one,

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it would be four times
that so I'm just going

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to approximate.

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Let's say that radius is four
times that so this is r two,

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which is equal to four times r one.

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And so we sketch in the radius
of this next radius here,

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this next allowed radius,
using the Bohr model.

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We could figure out mathematically
what that's equal to

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because we know r one is
equal to five point three

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times 10 to the negative 11 meters.

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And so if you do that calculation,
four times that number

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gives you approximately
two point one two times

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10 to the negative 10th meters.

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So this is our second radius
when n is equal to two.

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Let's do one more when n is equal to three

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so let's get a little bit more room here.

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So when n is equal to three,

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this radius will be equal to
three squared times r one.

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So once again, we're just taking three

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and plugging it into here

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and so three squared is, of course, nine.

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So this would be equal to nine times r one

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so our next allowed radius
will be nine times r one.

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And I'm sure I won't get this accurate,

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but it's a lot bigger.

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So this will be r three is
equal to nine times r one.

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So I won't even attempt
to draw in that circle,

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but you get the idea.

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And we could do that math
as well, so nine times

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five point three times 10
to the negative 11 meters

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would give you approximately
four point seven seven

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times 10 to the negative 10th meters.

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And so these are the
different allowed radii

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using the Bohr model so you
can say that the orbit radii

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are quantised, only
certain radii are allowed

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so you couldn't get something in between.

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You couldn't have something
in between in here

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according to the Bohr model
so this is not possible.

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And these radii are associated
with different energies

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and that's gonna be really important

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and that's really why we're
doing these calculations.

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So we're getting these
different radii here

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and each one of these radii is associated

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with a different energy.

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So, again, more to come
in the next few videos

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about energy, which is
probably more important.