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### Course: Modern Physics (Essentials) - Class 12th > Unit 3

Lesson 2: What makes neon signs glow in different colors?- Bohr's model of hydrogen
- Bohr model radii (derivation using physics)
- Bohr model radii
- Bohr model energy levels (derivation using physics)
- Bohr model energy levels
- Atomic Energy Levels
- Electronic transitions
- Bohr orbits: orbital radius and orbital speed
- Bohr model: energy levels

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# Bohr model radii

Using equation for Bohr model radii to draw shell model for n=1 to 3, and calculating the velocity of a ground state electron.

. Created by Jay.

## Want to join the conversation?

- Is this equation applicable only hydrogen atom?(35 votes)
- According to the equation -
**rn = n2*r1**

the radius when n = 1 =1*r1

the radius when n = 2 =4*r2

the radius when n = 3 =9*r3

So distance between K and L shell = 3r1

Distance between L and M shell is 5r1

However in periodic table we learn that the distance between the shells of an atom keep on decreasing but here they are increasing.

How?

Thanks.(6 votes)- Again, you can’t apply the Bohr model to other atoms.(12 votes)

- If the electrons have a specific range of distance from the nucleus, then that would mean that an electron could be actually anywhere inside that fixed "donut-shaped" orbit. Wouldn't it be very difficult for scientists to predict the actual position of an electron at a given time ?(2 votes)
- It is.

But the orbits aren't donut shaped.

And the Bohr model is not an accurate model.(8 votes)

- What are principal quantum numbers?(2 votes)
- principal quantum number is one of the four quantum numbers used to describe energy levels in the atom. it can have values n=1,2,3,4... and it determines the size of an orbital.(3 votes)

- FROM where did the Rydberg constant derived?(2 votes)
- Would the radius of the n= ∞ energy level be infinity?(1 vote)
- If you had to do this with the flow of the cell through the veins between the Right ankle to the left, How would you write that out? Since atom's function don't touch anything?(1 vote)
- The idea that atoms are mostly empty space or that nothing touches at an atomic level is not really accurate. Saying this you are using the loose idea of what empty space is and what it means to touch something in everyday life and not a technical scientific definition of what empty and touching means.

What is empty space? The concept of something occupying space come from our everyday concept of physical objects occupying a volume of space and that there is something there. When you start to look at things at an atomic and sub-atomic scales this idea starts to break down. Fundamental particles are essentially points with no volume that have associated fields that may or may not interact.

Saying that that matter particles don't ever occupy the same space and interact via fields but this is also true at every day macroscopic scales as well.

From a scientific perspective when you touch the surface of a table the electromagnetic fields and the Pauli exclusion principle come into play. As your finger gets closer to the table there is a slightly attractive force between the outer electrons in the atoms in your finger and the table and the nuclei in these atoms, this is called the van der Waals force. As the atoms in your finger and the table get even closer the Pauli exclusion principle begins to push the electrons in the atoms of your finger and the table apart. It is at the point where the Van der Waals force and the force from the Pauli exclusion principle cancel each other out it when your finger is technically touching the table.

So in the end the idea that matter is just empty space and things don't touch is not an accurate statement. It is using the more flexible common speech definition of touch in a way that it it doesn't apply.(2 votes)

- Is the radius REALLY a vector? I have a hard time visualizing it as such, and wonder if it isn't a scalar instead?(1 vote)
- I am not sure where in the video they refer to the radius as a vector. If you are assuming that because they put and arrow as the radius that may be the use of an engineering diagram convention of using an arow to show a dimension length.

There are cases where radius is used as a scalar and others where it is used as a vector. It sort of depends on the situation. For example is you are calculating the volume of a sphere r is scalar but when you are calculating the angular momentum of an object in circular motion it is a vector.(2 votes)

- does n represent the periods of the periodic table ? if not what ?(0 votes)
- no, it's just an integer that numbers the energy levels within the atom.(4 votes)

- In the video,is the r1 only for the hydrogen atom(Bohr's) or does it hold the same for all radii of the atoms

i.e is the r1 universal or does it change from element to element?

Thanks(1 vote)- Bohr model only applies to hydrogen and other one electron systems (eg He+, Li2+)(2 votes)

## Video transcript

- [Voiceover] If you
didn't watch the last video because there was too much physics, I'll just quickly summarize
what we talked about. We went over the Bohr
model of the hydrogen atom, which has one proton in its nucleus, so here's the positive
charge in the nucleus, and a negatively charged
electron orbiting the nucleus. And even though this is not reality, the Bohr model is not
exactly what's happening, it is a useful model to think about. And so we just assumed the electron was going in this direction So counter-clockwise around
which gives our electron a velocity tangent to our circle, which we said was v in the last video. And in the last video, we
calculated this radius. So we calculated the
radius of this circle, and we said this was equal to r one. So r one turned out to be five
point three times 10 to the negative eleventh meters,
which is an important number. And we also derived this equation, right. So r for any integer n is
equal to n squared times r one, for example, if you wanted
to calculate r one again. So the first allowed
radius using the Bohr model is equal to one squared times r one. And so obviously one squared
is one so r one is equal to five point three times 10 to
the negative eleven meters. And so when n is equal to one, we said this was an electron
in the ground state, in the lowest energy state for hydrogen. We'll talk about energy
states in the next two videos. So this is a very important number here. So this is, this number right here, is the radius of the smallest
orbit in the Bohr model. In the previous video, we
also calculated the velocity or we came up with an
equation that you could use to calculate the velocity
of that electron. If you go back to the previous video, you'll see the equation that
we derived was the velocity is equal to the integer n
times Planck's constant divided by two pi m times r, and we figured this out
using Bohr's assumption for quantised angular momentum and the classical idea
of angular momentum. So if we plug in some numbers here, we can actually solve for
the velocity of this electron cause we're gonna take
this radius and we're gonna plug it in down here and then we know what these other numbers are. So we said n was equal to
one, so we're talking about n is equal to one so we're
going to plug a one to here. So this will be a one. The velocity is equal to
one times Planck's constant, six point six two six
times 10 to the negative 34 divided by two pi times m. And we're talking about
the electron so m was the mass of our electron, which
is nine point one one times 10 to the negative 31st kilograms. And finally, for n is
equal to one, this was our allowed radius so we can
plug this in for our radius, five point three times
10 to the negative 11. So if you do all that
math, I won't take the time to do it here, but you'll get a velocity approximately equal to,
approximate sign, two point two times 10 to the sixth and
your units should work out to meters per second
so that's the velocity. So going by the Bohr
model, you can calculate the radius of this circle
here so you can calculate this radius, and you can
also calculate the velocity. And,again, this isn't
reality but we'll use these numbers in later videos so
it's important to figure out where they came from. So this is the radius of
the smallest orbit allowed using the Bohr model but
you can have other radii, and we can calculate the
radii of larger orbits using this equation. So we're just gonna use
different values for n. So we started off with n is equal to one. Let's use the same equation and let's do n is equal to two. So let me go ahead and rewrite
that equation down here. Let's get some room. So r for any integer n is
equal to n squared times r one. Let's do n is equal to two here. So n is equal to two so let's
go ahead and plug in two. So we'd have two squared times r one. So r two, the second
allowed radii or the second allowed radius I should say,
is equal to four times r one. So if we're thinking about a picture, let's say this is the nucleus here and then this tiny, little
radius here is r one. If we wanted to sketch in
the second allowed one, it would be four times
that so I'm just going to approximate. Let's say that radius is four
times that so this is r two, which is equal to four times r one. And so we sketch in the radius
of this next radius here, this next allowed radius,
using the Bohr model. We could figure out mathematically
what that's equal to because we know r one is
equal to five point three times 10 to the negative 11 meters. And so if you do that calculation,
four times that number gives you approximately
two point one two times 10 to the negative 10th meters. So this is our second radius
when n is equal to two. Let's do one more when n is equal to three so let's get a little bit more room here. So when n is equal to three, this radius will be equal to
three squared times r one. So once again, we're just taking three and plugging it into here and so three squared is, of course, nine. So this would be equal to nine times r one so our next allowed radius
will be nine times r one. And I'm sure I won't get this accurate, but it's a lot bigger. So this will be r three is
equal to nine times r one. So I won't even attempt
to draw in that circle, but you get the idea. And we could do that math
as well, so nine times five point three times 10
to the negative 11 meters would give you approximately
four point seven seven times 10 to the negative 10th meters. And so these are the
different allowed radii using the Bohr model so you
can say that the orbit radii are quantised, only
certain radii are allowed so you couldn't get something in between. You couldn't have something
in between in here according to the Bohr model
so this is not possible. And these radii are associated
with different energies and that's gonna be really important and that's really why we're
doing these calculations. So we're getting these
different radii here and each one of these radii is associated with a different energy. So, again, more to come
in the next few videos about energy, which is
probably more important.