The size of molecules

 

IN LAB, we've been using some material from "Explorations in Physics" by David Jackson, Priscilla Laws and Scott Franklin. (Creative Commons Share-Alike, attribution license), specifically, from their Unit C on Heat, Temperature, and Cloud Formation

The size of molecules

In this activity, we'll estimate the size of molecules (using pepper and soap, Section 2.1.1).

Here's a video of the demonstration (and calculation result) from a past class:

We're going to estimate the original size of the drop according to figure 2.6: a diameter of 0.3 mm. The radius of the sphere or drop on the hair, which I called $R$ in class, is $\approx 0.15$ mm=$1.5\times 10^{-4}$ meters.

    This year, Guliana and Christina measured across the region cleared of pepper to be approximately 14.5 cm (=145 mm = 0.145 meters). That means the radius of the soap pancake was 0.0725 meters.

Take this as roughly the *diameter* of a circle. Use this, and the diameter of the starting "drop" according to the lab photograph to estimate the height, $h$, of the 'pancake' of soap. This is our estimate of the maximum size of a soap molecule.

$$h=V/A=\frac{\frac 43 \pi 0.15^3}{\pi(17.5)^2}$$ This is 0.00001... mm

Desmos calculators

We'll use the Desmos 'scientific calculator' Download it from the Google Play store, or the App store for your phone or iPad. On a laptop, you can just go to desmos.com, scroll down and click on the Scientific Calculator.

Some nice features:

  • Works offline
  • When you divide, it displays a stacked fraction
  • Oh, mistyped a number? Or want to do the same calculation but with different numbers? You can erase & re-type any part of your calculation.
  • You can name the result of one calculation to use that result in a later calculation. For example, I might name the radius of our circular soap film, in meters, as $r$ like this: r=0.0725. Then later on I could calculate the area by writing out the formula, using my $r$, as A=pi*r^2. [In our temperature mixing, you might type m1=50 to get $m_1=50$

I'll also allow you to use the Desmos 'test' version of this calculator on exams / quizzes. Look for the app "Desmos test mode" in the stores.

To use it in an exam you can start the calculator in testmode and it locks you out of using other apps until you're finished. You show your phone, which displays how many minutes you remained in testmode, to your instructor at the end of the exam to prove you were unable to use the internet during the test.

No phone calls ring, no texts ping while you're in testmode. Hey, you can use it to prevent distractions while you're working on your homework anytime!