Bohr's Atomic Model — Overview & Importance

Bohr's Atomic Model

• In 1915, Danish physicist Niels Bohr proposed a new model of the atom.

What is Bohr’s Atomic Model?

• Bohr’s atomic model proposed that atoms contain orbits that electrons travel along. These orbits are quantized. So, they have a specific energy. The rate at which electrons travel depends upon the energy level of its orbit. You can imagine it like a solar system.

• As a side note, do not confuse these with orbitals. Orbitals are introduced in the quantum mechanical model which expands Bohr's model into three dimensions.

Bohr’s Atomic Model can be explained in a few points:

• An atom consists of orbits (or shells) that are quantized (have a set energy level and size), and these orbits are what electrons travel on.

• The energy level of an orbit is proportional to its size. So, a higher energy orbit will be bigger than a lower energy orbit.

• When an electron “jumps” between orbits, its energy level will change to the orbits energy level.

• Electrons are moving at a constant speed

• It is important to note that Bohr’s atomic model is not the most accurate atomic model available. Today we use the quantum mechanical model. An example of how Bohr’s atomic model is not entirely accurate is that it does not follow the Heisenberg Uncertainty Principle.

Why was Rutherford’s Atomic Model Disproved?

• In Rutherford's Nuclear Model it was originally thought that electrons orbit the nucleus of an atom. But, there was a problem. Rutherford applied classical electromagnetism. So the electron should be attracted to the nucleus. As the electron orbits it should accelerate. Because of the acceleration, the electrons should fall inward toward the nucleus. But, that would make any atom highly unstable! An atom would annihilate itself within picoseconds. In scientific notation that's $10^{-12}$! This was inexplicable because atoms in the natural world are stable.

• Because of this, Niels Bohr realized that the electrons in an atom are not accelerating. Instead, they must orbit around the nucleus at a fixed speed. The electron's energy depends on the orbit. But, for each orbit the energy is constant. It's similar to planets orbiting the sun.

Atomic Models

Through the years of the development of chemistry and the science as we know it today, the atom was of particular interest. Various scientists tried to model the atom based of scientific information gathered. As the field of quantum mechanics developed, more intricate and elaborate atomic models arose. One of the first models that included information discovered within quantum mechanics was proposed by Niels Bohr in 1914.

Bohr's Atomic Model

This atomic model depicted what Bohr believed to be the atomic structure of hydrogen. The model showed the nucleus being orbited by the electron, in a manner similar to planets orbiting the sun.

The Bohr atomic model was crucial because it explained that electrons only have specific energy levels available. However, as more electrons are added to the model, it becomes much less accurate. Also, this depiction does not take into account the wave-like nature of electrons. While, the Bohr model is not an accurate depiction of atomic structure, it is a historically significant model to the field of chemistry.

Bohr's Atomic Model

(Video) Bohr’s Model of an Atom | Atoms and Molecules | Don't Memorise

By: Don't Memorise

This video begins by comparing the Rutherford's atomic model to Bohr's atomic model. This video also goes into details about why Rutherford's model was disproven, and why Bohr's model was accepted. This video also discusses atomic shells, energy levels, and the structure of an atom.

We've been studying the history of chemistry. We're slowly building to the development of the quantum mechanical model of the atom. So far, we've been exploring how our perspective shifted away from classical physics. We started by looking at Planck's quantum theory. Then we saw Einstein solve the challenge of the photoelectric effect. We were beginning to understand that energy and matter behave differently at the atomic scale. This led to the development of the wave-particle duality. But, within chemistry, the central questions still revolved around the atom. We had various ideas like the plum pudding model and the nuclear model. But none of them truly fit the experimental data.

One of our remaining problems was atomic spectra. When we put energy into an atom, they emit different colors. But, various elements produced unique spectra. Could we develop a model that theoretically predicted these emission spectra? Thankfully, Niels Bohr had a unique insight into the structure of the atom. It didn't solve all the problems. But, it was a foundational first step.

Deriving the Bohr Model from Classical Physics

Let's study how Bohr derived his atomic model. He essentially only used classical physics. But, he made a momentous connection to quantum mechanics.

First, let's imagine a hydrogen atom. At its center is a positive charge. Remember, we didn't know about neutrons at the time. So, we thought the nucleus was just a proton. Hydrogen only has one electron. We'll imagine it orbiting the nucleus via circular motion.

Now, what is the total energy of the electron? The electron is moving. So, it has kinetic energy. But, there is also a potential energy component. It comes from the electrostatic attraction to the proton.

Do you remember the kinetic energy and Coulomb potential formulas from classical physics?

$K.E=\frac{1}{2}mv^{2}$.

• $m$ is the mass.

• $v$ is the velocity.

$P.E= \frac{KQ_{1}Q_{2}}{R}$.

• $K$ is Coulomb's constant. It equals $8.99\times 10^{9} \frac{Nm^{2}}{C^{2}}$. The units are Newtons-square meters over square Coulombs.

• Q is the charge in Coulombs. In this case, the charge of a proton and electron are equal but opposite. So, $Q_{1}Q_{2}\rightarrow e^{2}$. $e$ is $1.602\times 10^{-19}C$.

• R is the distance between the charges.

So, what's the total energy of the electron?

$E_{T}=K.E + P.E = \frac{1}{2}mv^{2} - \frac{Ke^{2}}{R}$

The negative sign comes from the electron's negative charge.

In our model, the electron is moving in a circular trajectory. The circular motion gets generated by the Coulomb force. It's like how gravity creates planetary orbits. That means the centripetal force (the force of circular motion) equals Coulomb's force. Remember, these are the force equations. So, they look different than the energy equations.

$\frac{mv^{2}}{R}=\frac{Ke^{2}}{R^{2}}$

If we solve for $mv^{2}$ we get $mv^{2}=\frac{Ke^{2}}{R}$

Let's plug that back into our energy equation.

$E_{T}=K.E + P.E = \frac{1}{2}mv^{2} - \frac{Ke^{2}}{R} \rightarrow \frac{Ke^{2}}{2R} - \frac{Ke^{2}}{R} \rightarrow \frac{-Ke^{2}}{2R}$

So, what are we left with? We have the energy in terms of the electron's charge and the distance between the proton and the electron. But how do we determine the distance within an atom? It's at this point that Bohr had his central insight. What if the electron's angular momentum is quantized? Remember, momentum is mass in motion. So, anything moving has momentum. Our electron is moving around the proton in a circular orbit. So, it has an orbital angular momentum. If angular momentum is quantized, we can relate it to multiples of Planck's constant.

$L=mvR=\frac{hn}{2\pi}$ where n=1,2,3...

• The $n$ and $h$ we saw in our study of black body radiation. All quantization is a multiple of Planck's constant. But what about the $2\pi$. It occurs because the electron is moving in a circle. A full circle is two-pi radians.

The trick here is to square the angular momentum.

$L^{2}=m^{2}v^{2}R^{2}=\frac{h^{2}n^{2}}{4\pi^{2}}$ where n=1,2,3...

Now, we can solve for $mv^{2}$.

$mv^{2}=\frac{h^{2}n^{2}}{4\pi^{2}mR^{2}}$ where n=1,2,3...

But we already had a relationship for $mv^{2}$! So, let's set them equal to each other.

$\frac{h^{2}n^{2}}{4\pi^{2}mR^{2}}=\frac{Ke^{2}}{R}$ where n=1,2,3...

What happens when we solve for R?

$R=\frac{h^{2}n^{2}}{4\pi^{2}mKe^{2}}$ where n=1,2,3...

But wait, h, $\pi$, m, K, and e are all constants! So, let's simplify.

$R=5.31\times 10^{-11}n^{2}$ where n=1,2,3...

Now we can plug R into our energy equation.

$E_{T}=\frac{-Ke^{2}}{2R}=\frac{-Ke^{2}}{2\times5.31\times 10^{-11}n^{2}}=\frac{-2.17\times10^{-18}J}{n^{2}}$ where n=1,2,3...

To make the units easier, we can convert joules to electronvolts.

$\frac{-2.17\times10^{-18}J}{n^{2}}\times\frac{6.242\times10^{18}eV}{1J}=\frac{-13.6eV}{n^{2}}$ where n=1,2,3...

What did Bohr's Model Accomplish?

We just derived the equation that Bohr proposed in 1913. But what does it actually tell us? It's the energy for each orbit of the hydrogen atom. Remember, at the time, we didn't know about orbitals. But it turns out that Bohr's model is a good prediction. How did we experimentally confirm Bohr's model? It theoretically predicted the atomic spectra of hydrogen! At the same time, other chemists were working on the modern periodic table. The Bohr model qualitatively fits some of the periodic trends. For example, it helped explain the octet rule, ionization energy, and atomic radius trends. Bohr's model was also the first step toward understanding valence electrons and covalent bonding. He proposed that molecules form between the outer orbit electrons of two atoms.

Imperfections of the Bohr Model

As you might guess, the Bohr model has some flaws. Why? There are a couple of reasons. The model does not account for electron-electron repulsion. The repulsion impacts the electron's energy. So, the energy levels are not the same for multiple electron systems. It also cannot describe the atomic spectra of heavier elements. Again the electron repulsion influences the wavelength of light emitted. Finally, it does not consider the wave-particle duality, the de Broglie equation, or the uncertainty principle. All of these would come within the next decade. They would transform the Bohr model into the quantum mechanical model!