Bohr Model

Up to now we have focused on the structure and the properties of the nucleus leaving electrons mostly out of the picture. In this next set of lessons we will explore the electrons in more depth and their contribution to an atom’s properties.

Quick History of Electrons

I won’t Bohr you with a lengthy history lesson (only bad jokes), but before jumping into the Bohr model itself we need to understand a couple of historical discoveries about electrons first.

The first is that the energy of both electrons and electromagnetic radiation (light, radio waves, etc.) come in fixed energy amounts called quanta. This means that photons and radio waves have certain allowable energy values. For example, a radio wave could carry 15 J or 25 J, but not 22 J. In this made-up scenario, the quanta that energy comes in is 5 J. So values that aren’t divisible by 5 wouldn’t be allowed.

The same is also true of electrons and this brings us to the second piece of information we have to understand. An electron’s energy is determined by its electric potential energy. This means the further away a minus charge (electron) is from a positive charge (nucleus) the higher its energy.

Electric potential energy is analogous to regular old gravitational potential energy.

Orbiting Like Planets

Since Bohr thought that the electrons orbited the nucleus like planets around the sun, this could only mean one thing! That electrons have fixed orbits around the nucleus positioned at specific distances called orbitals.

Ultimately, Bohr was wrong when the wave-particle duality of subatomic particles was discovered, but his model accurately predicts multiple features of an electron’s behavior so it is still useful.

Getting Excited

One thing the Bohr model is exceptionally good at explaining is how electrons absorb and emit energy. In general, electrons “live” in the most stable orbitals they can. The closer you get to the nucleus the lower the energy and the lower the energy the more stable the orbital is.

All of the electrons don’t fit in the first orbital though so an atom in its lowest energy state will occupy the closest orbitals that have space. This configuration is called an atom’s ground state and represents the most stable electronic configuration an atom can have.

When an atom absorbs energy it can jump up to a higher orbital in a process called absorption. However, each jump is quantized so an electron has to absorb just the right amount of energy to get to the next orbital. If the energy is either too great or too small then the electron won’t budge. This means that different elements and molecules only absorb specific amounts of energy.

Absorption Spectra

Typically the absorbed energy is in the form of photons, which are particles that represent electromagnetic radiation. These photons come in a variety of flavors from radio waves to gamma-rays with visible light and x-rays in between. Each photon carries a different amount of energy based on its frequency (Hz; f or ν) or wavelength (m; λ).

We can determine the exact relationship between energy, wavelength, and frequency using Planck’s equation. Here the h is Planck’s constant and is equal to 6.6 x 10-34 m2 kg / s.


As a result, elements can only absorb certain types of photons and each element has a unique combination of the photons it can absorb. This phenomenon can be exploited in order to determine the identity of a particular element. By shining full-spectrum visible light on a sample, we can measure what wavelengths are absorbed and which aren’t. Then we can compare the absorption spectra to a set of standards to determine which element our sample contains.

The dark bands indicate what light is absorbed from the full spectrum

Coming Down

What goes up must come down. When an electron jumps up to a higher orbital it enters an unstable excited state. As we saw from our exploration of isotopes, unstable atoms don’t tend to stick around. The same is true here except instead of losing electrons they just fall back down to the orbital they came from in a process called γ-decay.


In γ-decay an atom transitions from an excited state to its ground state by emitting a photon. Since we aren’t messing with the atom’s nucleus we won’t be moving anywhere new on the periodic table. Just transitioning from a high energy state to a low energy one.

This process is accompanied by the release of photons in order to obey conservation of energy in a process called emission. The energy that is released is equivalent to the energy that was lost when transitioning to a lower orbital. This means that elements have a unique emission spectra too!

The colored bands show what light is emitted

Emission Spectra

Just like absorption spectra, emission spectra are unique to each and every element. By exciting a sample’s electrons, we can measure what wavelengths are emitted and which aren’t and identify the element by comparing it to a standard as we did with absorption spectra.

The absorption and emission spectra should line up with dark bands becoming colored ones. This occurs because you can only emit what you were able to absorb.


Regardless of whether an electron is absorbing energy or emitting energy, it is transitioning from one orbital to another. Since these transitions are quantized we can calculate the exact amount of energy gained or lost in a transition. We have already seen one way of doing this using:


Since the energy of the transition is exactly equal to the photon energy either absorbed or emitted we can determine how much energy a transition required using the photon energy.

What if we want to predict the photon energy on the basis of a transition? We can’t use E=hf here because we don’t know the properties of the photon, such as its frequency or wavelength, ahead of time. However, the transitions between different orbitals are quantized and can be calculated using a different equation called the Rydberg formula. In this formula, ni refers to the starting orbital, nf to the ending orbital, and RH is the Rydberg constant (2.2 x 10-18 J/electron).

\[E=-R_H\left[ \frac{1}{n^2_i} – \frac{1}{n^2_f} \right] \]

Specific Series

The Bohr model was developed using the hydrogen atom since it is the simplest atom to model. As a result,t there are three characteristic groups of transitions we should know for the MCAT including the Lyman series, the Balmer series, and the Paschen series.

You could memorize the various values of the transition, but that is probably a waste of your time. It is more important to understand their general features, how they relate to one another, and what they predict about transitions in general.

First up let’s define each. The Lyman series represents transitions that start of end on n=1, the Balmer series transitions that start of end on n=2, and the Paschen series transitions that start or end on n=3.

From the image, we can see that the Lyman series produces or absorbs photons with the smallest wavelengths while the Paschen series produces or absorbs photons with the largest wavelengths.

\[E \propto \frac{1}{\lambda}\]

This means that the Lyman series produces or absorbs photons with the greatest amount of energy while the Paschen series produces or absorbs photons with the least amount of energy, with Balmer in between. Ultimately, the key determining factor in either energy absorbed or released is the lowest shell you start at or get to.

In general, a transition from n=1 to n=2 will always have more energy involved than a transition from n=2 to n=x or vice versa if we were going from high shells to low ones.

In The Real World

All of this talk about the Bohr model and electrons might seem really abstract. Turns out we have, in the normal course of our life, encountered all of these phenomena before even if we didn’t realize it. Furthermore, absorption and emission have important implications in research. We will talk about the exact techniques in later lessons but here we can begin to understand how this information is linked.


The color of objects is entirely determined by what types of light they do and don’t absorb. Here we were looking at atoms, but the electrons in molecules also absorb specific types of light. Take lycopene the compound that gives tomatoes their distinctive red color.


Due to its unique structure of alternating single and double bonds, it is able to absorb most wavelengths in the visible spectrum with the exception of red light. This red light doesn’t just pass through the tomato and end up somewhere else but bounces off the surface. When we look at a tomato this reflected light enters our eyes and as a result, we perceive tomatoes as red.

This phenomena can be used to monitor reactions that result in a color change. Such as Benedict’s test for reducing sugar which changes from blue to dark red if reducing sugars are present.


As described above certain molecules absorb specific wavelengths and how much light is absorbed varies from compound to compound. The amount of light absorbed is quantified as an absorbance value. These absorbances are frequently used in monitoring the progress of column chromatography among other research techniques.

For example, we might be trying to separate three differently sized molecules that all absorb the same wavelength using size exclusion chromatography. Since bigger molecules are able to absorb more light we could verify that a size exclusion column was working properly by monitoring the absorbance of the elutant.

We should expect to see smaller and smaller absorbances as the procedure continues since the largest molecules elute (fancy way of saying fall out of the tube) first and the smallest last.


Lastly, fluorescence is the emission of light by a substance after absorbing electromagnetic radiation. If you have seen a glow stick or like me had glow in the dark stars on your ceiling as a kid, you have experienced fluorescence. Unlike color, where certain wavelengths of light are absorbed or reflected light is emitted by the fluorescent substance. Think of the difference between a tomato in a dark room versus a tomato-shaped glow stick in a dark room.

In research, scientists add fluorescent tags or dye in order to keep track of particular molecules. For instance, we might want to track a specific protein and determine where it ends up in a cell. If we added a fluorescent tag during its synthesis we could then follow it around and see where it ultimately ends up.