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- [Voiceover] So in that last video,

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I showed you how to get this equation

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using a lot of Physics,

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and so it's actually
not necessary to watch

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the previous video, you can just start

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with this video if you want.

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And E one, we said, was
the energy associated

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with an electron,

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and the lowest energy level of hydrogen.

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And we're using the Bohr model.

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And we calculated the
value for that energy

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to be equal to negative 2.17 times 10

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to the negative 18 joules.

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And let's go ahead and convert
that into electron volts,

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it just makes the numbers
easier to work with.

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So one electron volt is equal to 1.6 times

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10 to the negative 19 joules.

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So if I take negative 2.17 times 10

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to the negative 18 joules,

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I know that for every one
electron volts, right,

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one electron volt is equal to 1.6 times 10

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to the negative 19 joules,

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and so I have a conversion factor here.

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And so, if I multiply these two together,

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the joules would cancel

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and give me electron volts as my units.

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And so if you do that math,

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you get negative 13.6 electron volts.

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So once again, that's
the energy associated

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with an electron, the lowest
energy level in hydrogen.

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And so I plug that back
into my equation here,

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and so I can just rewrite it,

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so this means the energy
at any energy level N

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is equal to E one, which is
negative 13.6 electron volts,

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and we divide that by N
squared, where N is an integer,

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so one, two, three, and so on.

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So the energy for the
first energy level, right,

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we already know what it is,
but let's go ahead and do it

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so you can see how to use this equation,

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is equal to negative 13.6 divided by,

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so we're saying the energy
where N is equal to one,

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so whatever number you have here,

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you're gonna plug in here.

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So this would just be
one squared, alright?

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Which is of course just one,

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and so this is negative
13.6 electron volts,

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so we already knew that one.

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Let's calculate the energy
for the second energy level,

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so E two, this would
just be negative 13.6,

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and now N is equal to two,
so this would be two squared,

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and when you do that math

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you get negative 3.4 electron volts.

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And then let's do one more.

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So the energy for the third energy level

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is equal to negative 13.6,
now N is equal to three,

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so this would be three squared,

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and this gives you negative
1.51 electron volts.

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So, we have the energies for
three different energy levels.

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The energy for the first energy level

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is equal to negative 13.6.

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E two is equal to negative 3.4,

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and E three is equal to
negative 1.51 electron volts.

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So energy is quantized
using the Bohr models,

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you can't have a value of energy
in between those energies.

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And also note that your
energies are negative,

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and so this turns out to
be the highest energy,

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because this is the one
that's closest to zero,

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so E three is the highest energy level

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out of the three that
we're talking about here.

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Alright, let's talk about the Bohr model

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of the hydrogen atom really fast.

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And so, over here on the left, alright,

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just to remind you, I already showed you

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how to get these different
radii for the Bohr model,

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so this isn't drawn perfectly to scale.

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But if we assume that we have
a positively charged nucleus,

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which I just marked in red here,

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so there's our positively charged nucleus.

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We know the electron orbits
the nucleus in the Bohr model.

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So I'm gonna draw an electron here,

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so again, not drawn to scale,

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orbiting the nucleus.

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So the positively charged nucleus

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attracts the negatively charged electron.

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And I'm saying that electron
is orbiting at R one,

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so that's this first radius right here.

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So R one is when N is equal to one,

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and we just calculated that energy.

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When N is equal to one,

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that was negative 13.6 electron volts,

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that's the energy associated
with that electron

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as it orbits the nucleus.

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And so if we go over here on the right,

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and we say this top line here represents

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energy is equal to zero,

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then this would be negative
13.6 electron volts.

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So none of this is drawn
perfectly to scale,

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but this is just to give you
an idea about what's happening.

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So this is when N is equal to one,

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the electron is at a distance
R one away from the nucleus,

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we're talking about
the first energy level,

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and there's an energy

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of negative 13.6 electron volts

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associated with that electron.

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Alright, let's say the
electron was located

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a distance R two from the nucleus.

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Alright, so that's N is equal to two,

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and we just calculated that energy

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is equal to negative 3.4
electron volts, alright?

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And then let's say the
electron was at R three

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from the nucleus, that's
when N is equal to three,

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and once again we just
calculated that energy

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to be equal to negative
1.51 electron volts.

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And so it's useful to compare
these two diagrams together,

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because we understand this
concept of energy much better.

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For example, let's say we
wanted to promote the electron

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that I drew, so this electron
right here I just marked.

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Let's say we wanted to
promote that electron

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from the lower energy level
to a higher energy level.

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So let's say we wanted
to add enough energy

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to cause that electron to go
from the first energy level

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to the second energy level,

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so that electron is jumping up here

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to the second energy level.

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We would have to give that
electron this much energy,

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so the difference in energy
between our two energy levels,

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so the difference between
these two numbers.

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And if you're thinking about
just in terms of magnitude,

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alright, 13.6 minus 3.4, alright?

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So this is a magnitude
of 10.2 electron volts.

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And so if you gave that
electron 10.2 electron volts

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of energy, right, you
could cause that electron

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to jump from the first energy level

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all the way here to the
second energy level.

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But you would have to provide
the exact right amounts

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of energy in order to get it to do that.

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Alright, let's say you
wanted to cause the electron

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to jump, let's say, from
the first energy level

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all the way to the third
energy level, alright?

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So from the first energy level
to the third energy level.

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So that would be, here's our electron

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in the first energy level,

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let's say we wanted to cause it to jump

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all the way up to here, alright?

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So once again, you would have to provide

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enough energy in order to do that.

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So, just thinking about
the magnitudes, right?

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This was negative 1.51,
this was negative 13.6,

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if we just take 13.6 minus 1.51, alright,

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we would get how much
energy we need to put in

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in order to cause that transition,

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so this would be 12.09 electron volts.

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And so if you gave an
electron 12.09 electron volts,

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you could promote it to
a higher energy level.

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And then finally, the last situation,

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let's think about taking the electron,

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let me go ahead and draw
it in here once more,

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in the first energy level.

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And let's say you provide
it with enough energy

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to take it an infinite
distance away from the nucleus,

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so again, not drawn to scale.

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So let's say we're at an infinite distance

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away from the nucleus.

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If the electron is infinitely
away from the nucleus,

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it feels no attractive pull.

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So there's no force,
there's no attractive force,

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we talked about Coulomb's Law earlier.

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So this is when R is
equal to infinity here,

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and if there's no attractive force,

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there's no potential energy.

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So the way we define potential energy,

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electrical potential
energy, it's equal to zero

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when R is equal to infinity.

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So the electrical potential
energy is equal to zero,

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and if it's not moving,

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then it's kinetic energy is equal to zero,

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and therefore it's total
energy is equal to zero.

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So this is what the diagram
over here on the right means.

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So when E is equal to zero,

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we're talking about the electron being

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an infinite distance
away from the nucleus,

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so we can say N is equal
to infinity, alright?

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R is equal to infinity,
and if it's not moving,

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it has a total energy equal to zero.

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So we've taken the
electron completely away

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from the nucleus, we
have ionized it, alright?

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So we've gone from a neutral hydrogen atom

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to the hydrogen ion, so
this turns it into H plus,

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so we're going from H to H plus.

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And that amount of energy,

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let me use a different
color here, so obviously

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it requires a lot of
energy in order to do that,

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so that would be going
from an electron here

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to an electron here, so
what is the magnitude

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of that energy difference?

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That's 13.6 electron volts.

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So it takes 13.6 electron
volts to take an electron

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away from the attractive
pull in the nucleus,

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and to turn it into an ion.

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And this number, 13.6 electron volts,

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corresponds to the ionization
energy for hydrogen.

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And so the Bohr model accurately predicts

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the ionization energy for hydrogen,

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and that's one of the
reasons why it's useful

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to study it and to think about

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these different energy levels.

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So not only are the
radii quantized, alright,

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just going back over here,

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not only are these radii quantized,

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but the energy levels are, too.