Modeling Ionization Energy with "Modeling Chemistry"

Simply Google ionization energy and you will quickly find a vast amount of images that appear like this--or at least similar to this:

To you and me, this image makes sense.  It makes sense in the context that it tells me so much about some of the properties of many of the elements.  But how do we get our students to interpret the numerous peaks and valleys within this image?  Better yet, how do we get our students to understand the reason for such peaks and valleys so that such an interpretation is valid?

For the sake of simplicity, ionization energy is the energy required to remove an electron from an atom.  I have no problem defining it this way in high school chemistry and I also have no problem simply giving students this definition.  I may even go into slight detail as to how this amount of energy is actually measured, just to make these numbers appear less dogmatic.  However, I do have a problem with giving them this definition and then simply showing them the trend (specifically, the 1st ionization energy trend) right off the bat.

How do we know this is the trend?  Why is this the trend?

I imagine many educators often adopt the use of actual ionization energy data for many elements, have students graph the ionization energies for each electron for a few elements, provide an explanation of the data with the Bohr model, use ideas such as Coulomb's Law to provide further explanation, and then call generally call it good.  To be honest, I don't really have any inherent disgust to this approach or anything.  Heck, it's pretty much what I do!  But I do think it leaves out (or limits) an important facet of science that we continuously try to help our students understand--the use of models to explain phenomena.  We give them the data, we give them the Bohr model explanation, we give them Coulomb's Law to help understand why an electron further away from the nucleus is easier to remove than an electron that is closer.

Where is the natural investigation in this?  Where are the individual ideas that the students have to provide explanation for this trend?  Where is the debate among competing ideas in class?  Where is the class consensus derived from their ideas?

To be clear, none of us honestly expect our students to provide some perfect explanation for such a trend based on their limited knowledge and application of such things like the Bohr model and Coulomb's Law.  So what do we do instead?  In my opinion, we provide a situation for them to create a model that, in general, provides an explanation for the data.  Such models are created in small groups, presented to the class, accepted or rejected based on their explanatory power, and then we come to a consensus on the best model.  All of this can be done without thinking of it in terms of atoms or the Bohr model--which itself has many faults in its explanatory power when it comes to ionization energy.

So here is how my chemistry classes approached the idea of ionization energy (not just 1st ionization energy) this year.

First, students were actually given the ionization energy data for each electron within the first 20 elements.  Students were then asked to graph the ionization energy (IE vs. # of electron) for each electron for Be, Si, and Ca.  This produces the following graphs:

What do we make of this?  Keep in mind that students have no idea of the "too-often-taught" 2-8-8 idea.  I have my own issues with that but I'll leave that alone for now.  We just picked 3 elements, graphed their ionization energies--do we notice any patterns?

1.) It appears that there are always 2 electrons that are REALLY hard to remove.  They are clearly in their own "group" and this appears in all 3 graphs.

2.) When supplied with enough electrons (as in Si & Ca) there seems to be a 2nd group that seems to consist of 8 electrons.  

3.) If we "zoom in" on the Ca graph by changing the y-axis max value, we notice that there is another group of 8 and then what appears to be another group of 2.  I must mention that this is where many students may often get the misconception that the 3rd energy level can only hold 8 electrons.  I tell them that, based on our evidence in front of us, this is so.  Later, when we investigate electron orbitals & configuration, that misconception gets resolved quickly.

At this point, the feature of the Bohr model that we are going to focus on and assimilate into our own model is the idea of different energy levels and the association energy required to remove an electron at such energy levels.  The model that we start to develop comes directly from the Modeling Instruction material and it is commonly known as the "men-in-the-well" model.  The reasoning behind it is rather simple and it goes a little something like this.

An energy well is drawn and a small stick figure is placed at the bottom like the image below.

energy well model of hydrogen atom

Person = electron

Getting the person out of the well is a metaphor for removing an electron from an atom, which requires energy.  The amount of energy required to pull out the person from the well depends on where the person is in the well and how deep the well actually is.  I'll go over a few examples and some of the original ideas that my students had but I think it's important to remember that the men-in-the-well idea is easy to visualize relative to the Bohr model.  Kids have past experience with pulling a friend or getting on someone's back to reach a higher spot.  They can actually imagine pulling someone out of a well and can easily distinguish which person would be easier to remove.  No experience in their lives can relate to what actually takes place at the quantum level within the Bohr model.  Therefore, we create this model to supplement what takes place at the atomic level.

So I show students what the model would look like for H and He.  It's incredibly important to stress to the students that the model must accurately reflect the data.  In other words, if one electron is easier to remove than another, my model must be able to explain that both visually (from the picture) and verbally (from the people who drew it).  So, below are the IE data for H and He.  All ionization energies are in electron-volts.

                                                                                            H             He

                                                                              1st       13.6         24.6  

                                                                              2nd       ---           54.4

After looking at this data, a couple things need to be explained.  

1.) Why is the 1st electron of hydrogen easier to remove than the 1st electron of helium?

2.) Why is the 2nd electron in helium more than 2x as hard to remove than its 1st electron?

Remember that even though we are using atomic data, we are NOT using atomic vocabulary in our models or explanations.  We're talking about people instead of electrons, depth of well instead of distance from nucleus, people helping each other get out instead of electron repulsion, etc.  So, I post this H and He data on the board and have the hydrogen "energy well model" shown.  

Instead of just telling them what I should do, I ask the students "how could I draw the well for the helium considering the fact that the 1st person in the helium well is harder to remove than the person in the hydrogen well?"

Honestly, it only takes a few seconds before several students simply say something like "make the well deeper".  Ok, so I make the well deeper and I get a comparison that looks something like this.

So we go back and try to see if this model accurately answers the first question:  Why is the 1st person in hydrogen easier to remove than the 1st person in helium?  The students easily agree that it's simply due to the fact that the helium well is deeper.  Makes sense.....but what about the 2nd question: Why is the 2nd person in helium so much harder to remove the 1st person in helium?  This is the beginning of when it starts to get creative and interesting with regard to their explanations.  Possible explanations have been

1.) Maybe the 1st person can jump higher to catch the rope hanging down

2.) Maybe the 1st person is taller

3.) Maybe the 1st person is stronger

4.) Maybe the 1st person is thrown upward by the 2nd person

5.) Maybe the 1st person gets on the back of the 2nd person to get up higher

6.) Maybe the 1st person stands on the shoulders of the 2nd person to get up higher.

After hearing a few potential explanations, I make one thing clear:

1.) All people (electrons) are the same in height, weight, strength, desire to want to leave, etc.

Having said this, it immediately gets rid of explanations like 1-3.  However, explanations 4-6 all have an important similar quality to them that should be recognized--they each involve the 1 person helping the other.  We start to focus on this idea for a bit and because it's easiest to draw, we settle on the explanation of the 1st person getting on the shoulder of the 2nd person in order to get higher up.  So even though the helium well is deeper, our model still makes sense if we assume the 2nd person in the helium well somehow helps the 1st person in the same well get out.  This explains why the 1st person is easier to remove from the well since the 2nd person has no one to help him.  We settle on this general approach and everyone seems to be satisfied with the explanation and the model.  

At the point, I should address to you that the students, by themselves, just naturally came up with the concept of electron repulsion.  I realize that they didn't use the words electron repulsion but coming up with this concept of 1 person helping the other to explain the data lays a solid foundation for when we start to include a concept like electron repulsion.  It won't be hard for students to just be like, "oh, that's like when the people were helping each other out of the well."  Building these models helps our students assimilate certain concepts that they constructed within their own mind into somewhat difficult concepts more easily, like electron repulsion.

Ok, so now we have accurate models that we all agree on that represent H and He.  But what about the other elements?  What about lithium and beryllium?  At this point, I split the class into several groups of about 2-3 students each.  On their whiteboards, they are to present the following things:

1.) IE data for Li and Be

2.) Energy well model for Li and Be

3.) Either a brief written explanation on your board OR just rely on your own verbal skills to provide an explanation orally.  

I'll give you 10-12 mins.....GO!

Here is the IE data for Li and Be:

                                                                                          Li             Be

                                                                1st                     5.4            9.3

                                                                2nd                   75.6          18.2

                                                                3rd                    122           154

                                                                4th                     ----           218

A couple things to address:

1.) 1st person in Li easier to remove than 1st person in Be

2.) Why the HUGE drop between 1st and 2nd people in Li and the HUGE drop between 2nd and 3rd people in Be?

3.) Why is the 2nd person in Be easier to remove than the 2nd person in Li?

Here are a couple whiteboards representing slightly different and creative ideas:

As a teacher, the most fascinating part about letting the students come up with their own explanations is what occurred in the bottom whiteboard.  Within that group, they could not come to an agreement.  Two girls had one idea while the other 2 girls had a different idea.  In other words, they had two competing theories.  I told them to put both on the board and let the class decide which theory has better explanatory power.  THIS IS HOW SCIENCE IS DONE!!!!!

Anyways.....take another look at the boards and see what students came up with on their own--the idea of energy levels!!!  At no point in time did I tell them they needed to add a step or some sort of board sticking out the side of the well.  Using their own reasoning and bit of creativity, they came up with this idea that within the well are boards that the people can stand on that allow them to be higher up and therefore easier to remove.  Pretty cool!  Now that they have this concept created, it will be way to easier to understand the idea of electrons occupying energy levels further away from the nucleus are easier to remove than ones closer.  

Though I could type out the merits and faults of each model presented, it would take too long and chances are, you can see some of them for yourself.  However, I will say we had a really good debate in class about which models more accurately represented the data.  In the end, we naturally arrived at a series of models that looked something like this:

We believed these models were sufficient because they were able to explain the original questions we posed:

1.) The 1st person in Li is easier to remove than the 1st person in Be because the 1st person in Li is up higher.

2.) The HUGE gap between the 1st and 2nd persons in Li can be explained by the fact that the 1st person is up on some sort of shelf or board sticking out of the side of the well which allows him to be much higher up than the 2nd and 3rd persons.  Same thing goes for the 1st and 2nd persons in Be compared the the 3rd and 4th persons in the same well.

3.) The 2nd person in Be is easier to remove than the 2nd person in Li because he is higher up.

In addition.....

4.) The 1st person in Be is easier to remove than the 2nd person in Be because the 2nd person helps the 1st person escape.  Same thing goes for the 3rd person compared to the 4th person.

5.) Remember those 2 electrons that kept showing up isolated in the top right corner of the graphs earlier?  Our energy well model accounts for those 2 electrons by consistently putting them at the bottom of the well since they're the hardest to remove.  This sets the stage for the number of electrons that can occupy an energy level.  If you were to keep going with these energy well models, you find that a max of 8 people should fit on the next shelf in the well.  Again, the model is naturally building the foundation for scientific concepts that we will be talking about later (like electron configuration, bohr model, and even how electrons move from different energy levels.

We continue to draw models and provide explanations for every bit of detail for most of the 1st 20 elements.  Like most models, these energy well models have faults.  For example, it doesn't take into account the different type of orbitals that exist within certain energy levels.  When certain anomalies come up where we can't quite use our models to explain the data, I simply tell them that they will get resolved later.  They do  eventually get resolved once we get into electron configuration.

What was cool about introducing ionization energy patterns this way was the inclusion that was given to the students.  I introduced a model that we could work with and they just sort of ran with it and edited it in order to better explain the data.  Some worked out while others didn't.  We had conversations about why one model was better than the other and we eventually came to a consensus on the most accurate of models.  This is the process we want our students to experience when we introduce different scientific concepts mainly because this is how science is actually done.  I have no doubt that many of the students would've been just fine if I had just explained to them the ideas of electron repulsion, energy levels, and Coulomb's law but the whole process of discovery, failure, and discourse would've been substituted with a much more dogmatic approach.  The more we can include our students in the investigation and the process of understanding how certain concepts can be understood, the more fun we can have in the class and the deeper the overall understanding can be.