It started with a short in-class question. If you know the mass of one mole of platinum and the density of platinum, what is an estimate for the diameter of one platinum atom? Of course, this calculation involves some assumptions. The primary assumption is that the platinum atoms form a cubic lattice such that the diameter of an atom would be the same length as one side of the cube of space it takes up.
It isn't a terribly difficult question, but still students will make mistakes. One of the early student responses I saw said that the atom diameter would be 5.4 x 1018 meters. And I thought the red Angry Bird was big....
How Wrong Is Wrong?
Just for fun (and because I was curious), I made this histogram of all of the student answers. I know you can't really take the natural log of something like a diameter (because it has units) - but you get the idea. Oh, the value based on the given density of platinum would have ln(d) = -22.
As you can see, many students did indeed have the correct answer (or at least close to the same order of magnitude). There are some students that are off by a factor of 100 because they incorrectly converted centimeters to meters. The two largest answers were 6.69 x 1028 m and 5.4 x 1018 m. The smallest response was 1.8 x 10-25 m.
Let me just throw out some numbers for comparison.
- The distance across the Milky Way Galaxy is about 1021 meters.
- The Andromeda Galaxy is about 2 x 1022 meters from here.
- The distance to the Sun from the Earth is about 1011 meters.
- The Earth is about 107 meters.
I don't expect students to know all these values. However, they should know that people-sized things are on the order of a meter but something like 107 meters isn't anywhere close to people sized let alone atom-sized.
What Is The Problem?
After a short twitter discussion, Brian Utter commented:
This is so true. All too often, we set things up for students such they never have to make these evaluations. I think there are some other problems. People tend to think that 107 is sort of like 7 times bigger than 10. If you ask them a direct question regarding this, they won't say that. However they can fall into a trap regarding this.
Perhaps just addressing issues like this in class can help. Maybe even better is to present students situations where they can evaluate answers. They can look at other students' work and they can look at their own work. If that presents logistical questions, the instructor could create answers with (or without) errors for the students to evaluate. I think that is where I am going to start.
Let me leave you with one more great tweet about large answers.
Powers of Ten
You know I couldn't let this go without including the famous "Powers of Ten" video. However, I posted the 1977 version of this video and it was rejected by my students. They liked this Morgan Freeman version much better.
