In the **Bohr Model**, electrons can move up and down to different orbitals or shells based on absorbing or releasing of energy.

Bohr Model

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concept

## Bohr Model

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Now in the boar model of the atom, electrons travel around the nucleus in circular orbits, which we call shells. Now these shells used the variable end and a shell is just a grouping of electrons surrounding the nucleus that ties into their potential energy. So their energy of position, we're gonna say associated with boards model is what we call the Rydberg constant. And when it's dealing with jewels, the value is 2.178 times 10 to the negative 18 as the value for Rydberg constant. Now, if we're looking at boards model, remember, in our boards model, we have our nucleus here in orange and within the nucleus. Remember, That's where we find our protons and our neutrons. Remember, protons are positively charged. Neutrons are negatively charged. Orbiting around the nucleus in these orbits or shells are are electrons. Remember, electrons themselves are negatively charged. And we're going to say if we take a look, here's our nucleus. This is our first orbit or our first shell so n equals one. This is our second orbit, where we find three more electrons. So this is shell to, and this would be shell three. And remember here we said Shell, it uses the variable end and we're gonna say n equals R shell number, but also what we call our energy level. We're going in greater context in terms of that, when we talk about the quantum numbers Now, how do we tie this into the energy of a particular electron? Because, remember, we said that the shell number ties into their potential energy. Well, we're going to say here the energy of an electron within a specific shell can determined by Delta, E or E N, which is the potential energy of an electron equals negative times are, which is our right Burt Constant, which we said is 2.178 times 10 to the negative jewels. And that's gonna be times Z squared over and squared. Z here equals the atomic number of an element. For example, hydrogen first element on the periodic table has an atomic number of one and then n squared on the bottom, remember, and would just be the shell number or energy level for that particular electron. So just remember, electrons travel within orbits around the nucleus, and by using this potential energy formula, you could determine the potential energy associated with any particular electron within a given. Adam

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example

## Bohr Model Example 1

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here in this to counted the energy of an electron found in the second shell of the hydrogen atom. Alright, since we're looking for the energy of an electron within a given shell, we're looking for its potential energy. It's energy of position. So Delta e equals negative are times Z squared over and squared. Our is our riper constant. So that's negative. 2.178 times 10 to the negative 18 jewels. Z equals the atomic number of the element. Since its hydrogen, its atomic number is one so that be one squared, divided by and squared. Remember? And here is the energy level or shell number. They tell us that the second shell so and equals two. So I'd be two squared. So here, that's negative. 2.178 times 10 to the negative. 18 Jules one squared is just 12 squared is four. So that comes out to negative 5. times 10 to the negative 19 jewels. Since it doesn't give us a number of sig figs in the beginning of the question at all, we could determine our own number of Sig figs here. I'm just going with four significant figures in terms of the potential energy for that particular electron

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concept

## Bohr Model

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now within a given Adam. We confined electrons within given orbits or shells, but realize through either the absorption or mission of energy, electrons are able to move between these different shells. Now, when we talk about absorption and emission, what exactly do we mean? Well, when we say absorption, this is one electron moves from a lower numbered shell toe are higher numbered shell, and the mission is when the electron does the opposite. It's one electron moves from a higher number of shell to a lower numbers show every word to visually see this. Here we have absorption in the first image. Here in absorption. We're going to say the electron absorbs energy, So basically, we have some outside energy source displayed as this energetic photon. That photon is giving its energy to this electron. This electron is initially in the first orbit of the atom, so it's in shell one. It absorbs this energy, and it allows it to a jump upto a higher energy state, which we call the excited state. So this electron is able to, in this example, go from the first shell to the third shell. Now, if absorption is going up to a higher level. Emission is the opposite here realize that that electron can't hold on to that outside energy forever. Eventually it has to let it go. So here the electron emits or what we say releases this excess energy it got from earlier. When it does so, it's gonna fall back down to its original position, which we call its ground state. So here the electron goals from the third shell and goes right back down to its initial position, which is shell one. But how does this relate? How hard is it for electrons to travel between these shells? Well, here we talk about energy transitions were saying here, As the shell number increases, the distance between them is going to decrease. So if you look, this is shell 1234 and five. The distance between shells one and two is this big distance. Here. The distance between two and three is this is this is between four and five. Is this and then you can see that the distance is getting smaller and smaller. The higher up we go in terms of shell number. That's because as the distance traveled by an electron is increasing the than Mawr energy is needed, the energy increases. So basically, what we're saying here is that traveling between shells one and two requires the most energy look at the distance. It has to travel from here all the way up to here. And if we wanted to go from shell, one is shell three. That's an even bigger cost. If you're trying to go from Shell one, all we have to shell three. Look how much bigger the distances. But then, as we're starting up at a higher shell number, less energy is required. So let's say we wanted to go from Shell 3 to 5. Not as much energy is required. So just realize that distance equals energy. The more electron has to travel in the greater amount of energy is needed and realize. Here is the shell number increases than the distance between the shells get smaller. So it's easier front electron to go from, Let's say, shell six to Shell seven than it is from going from shell one to shell, too.

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Problem

Which of the electron transitions represents absorption with the greatest frequency?

A

n = 5 to n = 3

B

n = 1 to n =3

C

n = 2 to n = 4

D

n = 6 to n = 7

E

n = 4 to n = 5

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Problem

Which of the following transitions (in a hydrogen atom) represent emission of the shortest wavelength?

A

n = 3 to n = 1

B

n = 2 to n = 4

C

n = 1 to n = 4

D

n = 5 to n = 3

E

n = 2 to n = 5

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Problem

If the energy of an electron within the boron atom was calculated as –6.0556 x 10^{-18} J, at what energy level would it reside?

A

2

B

3

C

4

D

5

Additional resources for Bohr Model

PRACTICE PROBLEMS AND ACTIVITIES (14)

- Which arrow in the energy diagram for an atom represents the absorption of light with the shortest wavelength?...
- Consider the three electronic transitions in a hydrogen atom shown here, labeled A, B, and C. (a) Three electr...
- Does the hydrogen atom “expand” or “contract” when an electron is excited from the n = 1 state to the n = 3 st...
- Classify each of the following statements as either true or false: (a) A hydrogen atom in the n = 3 state can ...
- Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? (b) from an orbit o...
- Is energy emitted or absorbed when the following electronic transitions occur in hydrogen? (a) from n = 3 to ...
- Indicate whether energy is emitted or absorbed when the following electronic transitions occur in hydrogen: (a...
- (a) Using Equation 6.5, calculate the energy of an electron in the hydrogen atom when n = 3 and when n = 6. Ca...
- Consider a transition of the electron in the hydrogen atom from n = 8 to n = 3. (b) Will the light be absorbed...
- The hydrogen atom can absorb light of wavelength 1094 nm. (b) Determine the final value of n associated with t...
- Order the following transitions in the hydrogen atom from smallest to largest frequency of light absorbed: n =...
- Determine whether each transition in the hydrogen atom corresponds to absorption or emission of energy. a. n =...
- Ionization involves completely removing an electron from an atom. How much energy is required to ionize a hydr...
- Bohr’s model can be used for hydrogen-like ions—ions that have only one electron, such as He + and Li2 + . (a)...