Bohr Model - Online Tutor, Practice Problems & Exam Prep

In the Bohr model of the atom, electrons orbit the nucleus in defined paths known as shells, each with a specific energy level denoted by the principal quantum number (n). The potential energy of an electron in a shell is given by the equation:

$E_n=-R(Z^2/n^2)$

where R is the Rydberg constant (2.178 x 10^-18 J), Z is the atomic number, and n is the shell number. Electrons can transition between shells by absorbing or emitting energy, with absorption moving an electron to a higher energy shell and emission returning it to a lower one. The energy required for these transitions depends on the distance between shells; the greater the distance, the more energy needed. As shell numbers increase, the distance between them decreases, requiring less energy for an electron to move between higher shells. This concept is critical for understanding atomic structure and electron behavior.

Bohr Model

Now in the Bohr model of the atom, electrons travel around a 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 going to say associated with Bohr's model is what we call the Rydberg constant. And when it's dealing with joules, the value is 2.178×10-18 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 = 1. This is our second orbit where we find three more electrons. So this is shell two and this would be shell three.

And remember here we said shell uses the variable N and we're going to 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, 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 ΔE or EN which is the potential energy of an electron equals negative times R which is our Rydberg constant which we said is 2.178×10-18 Joules And that's going to be times Z2 / N2 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 N2 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.

Bohr Model Example 1

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 ΔE=-R∗Z2/N2. R is our Ryberg constant, so that's -2.178∗10-18 J. Z equals the atomic number of the element. Since it's hydrogen, its atomic number is 1, so that would be 12/N2. Remember N here is the energy level or shell number. They tell us it's the second shell, so N = 2, so that would be 22.

So here that's -2.178∗10-18 J. 12 is just one. 22 is 4, so that comes out to -5.445∗10-19 J. 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 four significant figures in terms of the potential energy for that particular electron.

Bohr Model

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 were 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 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 going to fall back down to its original position, which we call its ground state. So here the electron goes from the third shell 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. We're seeing 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 one and two is this big distance. Here the distance between 2 and 3 is this. The distance between 4 and 5 is this. And then you can see that the distance is getting smaller and smaller the higher we go in terms of shell number.

That's because as the distance traveled by an electron is increasing, then more 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 to shell three, that's an even bigger cost. If you're trying to go from shell one all the way up to shell three, 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 an 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 one to shell 2.

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

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

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

Here’s what students ask on this topic:

What is the Bohr model?

The Bohr model, proposed by Niels Bohr in 1913, is a theory for the hydrogen atom based on quantum theory that energy is transferred only in certain well-defined quantities. It posits that electrons orbit the nucleus in discrete, stable orbits with specific, fixed energies. This was a significant advancement from the earlier Rutherford model, which couldn't explain why atoms emitted light in specific wavelengths or why electrons weren't pulled into the nucleus.

Bohr suggested that as long as an electron remains in its orbit, it does not radiate energy. However, it can jump from one energy level to another, and when it does, it either absorbs or emits a photon with energy equal to the difference between the two levels. This model introduced the concept of quantization in the atomic structure, which was a fundamental step towards the development of quantum mechanics. However, the Bohr model only accurately describes the hydrogen atom and is oversimplified for more complex atoms.

How did Niels Bohr describe electrons in his atomic model?

Niels Bohr, building upon Rutherford's atomic model, proposed that electrons orbit the nucleus in distinct energy levels, which he referred to as "shells" or "orbits." According to Bohr's atomic model, these electrons could only occupy certain allowed orbits where they would not emit radiation. However, they could jump from one energy level to another, a process accompanied by the absorption or emission of a quantum of electromagnetic radiation, which we observe as light or other forms of electromagnetic waves.

Bohr's model was revolutionary because it introduced the concept of quantization in the structure of the atom, meaning that the electrons' energy was quantized, existing in discrete levels rather than a continuous spectrum. This model successfully explained the spectral lines of hydrogen but had limitations when applied to more complex atoms. Despite its limitations, Bohr's model was a significant step forward in the development of quantum mechanics and our understanding of atomic structure.

How do you draw a Bohr model?

To draw a Bohr model for an atom, follow these steps:

1. Determine the Number of Electrons: Find out how many electrons the atom has. This is equal to the atomic number of the element, which you can find on the periodic table.
2. Draw the Nucleus: In the center of your paper, draw a circle to represent the nucleus. Inside it, write the symbol of the element you're drawing.
3. Add Electron Shells: Around the nucleus, draw concentric circles to represent the electron shells. Each shell can hold a certain number of electrons: the first can hold up to 2, the second up to 8, the third up to 18, and so on.
4. Place Electrons: Starting with the innermost shell, place dots around the circles to represent electrons. Fill each shell according to its capacity before moving to the next one.
5. Check Your Work: Ensure that the total number of electrons equals the atomic number of the element. The Bohr model is a simplified representation and works well for explaining atoms up to calcium (with atomic number 20). For elements with more electrons, the model becomes less accurate due to the complexities of subshell filling and electron repulsion.