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 Bohr model of the atom, electrons travel around the nucleus in circular orbits, which we call shells. Now these shells use the variable n 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 Bohr's model is what we call the Rydberg constant. And when it's dealing with joules, the value is 2.178 times 10 to the negative 18 as the value for Rydberg constant. Now if we're looking at Bohr's model, remember in our Bohr's 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 our 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 1. This is our second orbit where we find 3 more electrons, so this is shell 2, and this would be shell 3. And remember here we said shell uses the variable n, and we're gonna say n equals our shell number, but also what we call our energy level. We'll go in greater context in terms of that when we talk about the quantum numbers. Now if 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 be determined by delta e or e n, which is the potential energy of an electron, equals negative times r, which is our Rydberg constant, which we said is 2.178 times 10 to the negative 18 joules, and that's gonna be times z squared over n squared. Z here equals the atomic number of an element. For example, hydrogen, first element on the periodic table has an atomic number of 1. And then n squared on the bottom, remember n 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 can determine the potential energy associated with any particular electron within a given atom.
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example
Bohr Model Example 1
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Here it is to calculate 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, its energy of position. So delta e equals negative r times z squared over n squared. R is our Rydberg constant, so that's negative 2.178 times 10 to the negative 18 joules. Z equals the atomic number of the element. Since it's hydrogen, its atomic number is 1, so that'd be 1 squared, divided by n squared. Remember, n here is the energy level or shell number. They tell us it's the second shell, so n equals 2. So that'd be 2 squared. So here that's negative 2.17 7 8 times 10 to the negative 18 joules, 1 squared is just 1, 2 squared is 4. So that comes out to negative 5.445 times 10 to the negative 19 joules. Since it doesn't give us a number of sig figs in the beginning of the question at all, we can determine our own number of sig figs. Here I'm just going with 4 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 atom, we can find electrons within given orbits or shells, but realize through either the absorption or emission 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 when an electron moves from a lower numbered shell to a higher numbered shell, and emission is when the electron does the opposite. It's when an electron moves from a higher numbered shell to a lower numbered shell. If we're to visually see this, here we have absorption in the first image. Here in absorption we're gonna 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 1. It absorbs this energy and allows it to jump up to 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 goes from the 3rd shell and goes right back down to its initial position which is shell 1. But how does this relate? How hard is it for electrons to travel between these shells? Well, here we talk about energy transitions. We're saying here as the shell number increases the distance between them is going to decrease. So if you look, this is shell 1, 2, 3, 4, and 5. The distance between shells 12 is this big distance here. The distance between 23 is this, the distance between 45 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 a distance traveled by an electron is increasing the then more energy is needed, the energy increases. So basically what we're saying here is that traveling between shells 12 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 1 to shell 3 that's an even bigger cost. If you're trying to go from shell 1 all the way up to shell 3, look how much bigger the distance is. 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 then the greater amount of energy is needed. And realize here as the shell number increases then the distance between the shells gets smaller. So it's easier for an electron to go from, let's say, shell 6 to shell 7 than it is from going from shell 1 to shell 2.
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Problem
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
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
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?