Unit #1

Activity 2
The Power of Thinking in Powers of Ten

Activity Overview

Understanding the microscopic world of atoms requires having some sense of scale to compare the visual world to that of the tiny atom.

Students use Workbench software to get a visual sense of the relationship between powers of ten and objects of that size.

Then students go to a web site where they can do virtual electron microscopy. While observing various items with their virtual electron microscope students are asked to indicate how many orders of magnitude difference there are between the lowest and highest power magnification.

Learning Objectives

Students will:

• Identify a number that is written in exponential notation as very large or very small.
  
• Describe the size of atoms correctly as very, very, small.

Conceptual Prologue

Macro-Micro Connection

The extremely small size of an atom is one characteristic which is important for understanding their behavior and the resulting observations we make. This activity tries to give students a general sense that atoms are really, really small. That is why we don't see atoms in our hot air balloon (or anywhere else) when making observations with our naked eyes. Fluid substances like air (inside the balloon) or water don't feel grainy because the grains making up these substances are extremely small. Even the surface of a highly polished solid is more like a piece of sandpaper when observed at the atomic scale. This activity tries to help explain why we think atoms exist even if we don't commonly observe them - they are just too small.

Science Concepts

Numerically it can be very cumbersome to describe extremely large or small sizes. Our galaxy is about 1000000000000000000000000000 meters across while an atom is about 0.0000000001 meters across. There is a way to easily represent numbers of large or small magnitude - exponential notation.

The diameter of our galaxy is 1 followed by 27 zeros. This can be represented by the number 1 x 10²⁷ or simply 10²⁷ meters. The diameter of a typical atom can be represented by 1 x 10^-10 or simply 10^-10 meters. If the exponent is positive then multiply by 10 the number of times described by the exponent. If the exponent is negative then divide by 10 the number of times described by the exponent.

The difference between multiplying by 10 or dividing by 10 is called an order of magnitude or a “power of ten”. For example, 100 (10²) is one order of magnitude or power of ten higher than 10 (10¹) and two orders of magnitude or powers of ten higher than 1 (10⁰). The number 1,000 (10³) is three orders of magnitude or powers of ten lower than 1,000,000 (10⁶).

Naive Conceptions

• Numbers like 1,000,000,000 (10⁹) or 0.00000001 (10^-8) can be intuitively understood.

Very large and very small numbers are, for the most part, incomprehensible in any realistic sense. They can be written down using exponential notation, and understood as very large or very small, but that is about the limit. Students have a hard time comprehending that atoms are too small to see.

Activity Design and Execution

Major Science Concepts:	•orders of magnitude, exponential notation
Assumed Previous Knowledge:	• Substances consist of atoms.
Time:	• Approximately 50 minutes
Materials:	• Computers with Workbench software. • Computers with an internet connection and a browser (preferably Internet Explorer)
Advanced Preparation: (if any)	• none

Investigative Question: How big is an atom?

1. Explain to students how exponential notation represents large and small numbers. Have them do a few examples.
2. Have students use the Workbench software to zoom up and down through various magnifications. The software will ask students to note which power of ten represents a distance equal to the image on the screen.
3. Have students go to the following web site: http://micro.magnet.fsu.edu/primer/java/electronmicroscopy/magnify1/index.html
4. Ask them to choose several different objects to explore with the virtual electron microscope. Have them indicate how many orders of magnitude difference there are between the lowest magnification and the highest.
5. Explain to them that even an electron microscope can’t “see” atoms because the atoms are much smaller than the microscope’s highest magnification.

Assessment

Have students write several things in their notebooks:

1. Translate the following numbers to either exponential notation or normal notation:
   10⁹, 10^-6, 10000, 0.00000001
2. Which is bigger 10⁷ or 10⁹?
3. Which is smaller 10^-7 or 10^-9?
4. How small are atoms? What number represents the size of an atom, measured in meters.
5. Which power of ten best describes the size of a hot air balloon: 10¹, 10², or 10³ meters?