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Powers of 10  How Small Is an Atom? (2 Favorites)
ACTIVITY in Measurements, Scientific Notation, Atomic Radius. Last updated December 10, 2020.
Summary
In this activity, students will use an online interactive to investigate the size of an atom, and compare the size of the atom to other objects using scientific notation.
Grade Level
Middle School, High School
NGSS Alignment
This activity will help prepare your students to meet the following scientific and engineering practices:
 Scientific and Engineering Practices:
 Using Mathematics and Computational Thinking
 Developing and Using Models
Objectives
By the end of this activity, students should be able to:
 Compare the size of an atom (qualitatively) to other objects
 Compare the size of an atom (quantitatively) to other objects, using scientific notation
Chemistry Topics
This activity supports students’ understanding of:
 Atomic structure
 Atomic scale
 Atomic radius
 Measurement
 Scientific notation
Time
Teacher Preparation: 15 minutes
Lesson: 45 minutes
Materials
 Device with internet access (phones will work, but larger screen is preferred); http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html
 Whiteboards for each group (34 students per group) and dry erase markers (large paper may be substituted if whiteboards are not available)
 Student handout
Safety
 No specific safety precautions need to be observed for this activity.
Teacher Notes
 I use this activity to help students build fundamental understanding about atoms and atomic structure at the beginning of the school year.
 Typically, I begin with the “Golden Penny” lab (can we actually coat a penny with gold?) which provides us with a starting point for our discussions on atoms. (This experiment can be found as part of The Captivating Chemistry of Coins lesson plan.) After we have established, as a class, that gold is made of only gold atoms, we begin to have conversations about exactly what atoms are, and start with a basic definition that atoms are the smallest piece of matter that still retains the properties of the element.
 Students have most likely used exponents and scientific notation in their math classes, but they may need a refresher, and many have not had to use exponents outside of a math classroom. As they will be using scientific notation many times in chemistry, this is a good time to review it and establish how it is used in the context of chemistry. If you feel your students would benefit from reviewing it in more detail before completing this activity, you could use this Scientific Notation activity first to review writing numbers in scientific notation, and/or this lesson plan on Using Scientific Notation in Chemistry. These would be particularly useful for the “Challenge Questions” at the end, which require them to put numbers into scientific notation and do calculations with them.
 The first guiding question for the students will be: “If we could split a piece of gold into smaller and smaller pieces, how small could we get  and have it still be gold?” Start this activity with a class discussion about this first question. Most students know that an atom is the correct answer, but do not know how small an atom actually is.
 Have students break into small groups to discuss the question “how small is an atom,” and make a prediction on their whiteboards. This is outlined in step 1 of the student instructions. Call on groups to provide their predictions, and post them somewhere in the classroom for later. They may not be able to express these in scientific notation yet, just fractions, and this would be a good time to introduce turning these into scientific notations. (Ex: if a student predicts that an atom is 1/1 millionth of a meter, show them how to write this as 1.0 x 10^{–}^{6})
 Although there may be some students who already have a good idea of just how small an atom is, many students struggle when trying to compare an atom to other objects. (Many students could not correctly compare an atom to a grain of sand.) This is outlined in step 2 of the student instructions. After each group predicts the placement of each item on their whiteboards (smaller than an atom of gold, larger than an atom of gold) allow them to work with the interactive before reviewing answers as a class. This is outlined in step 3 of the student instructions. The website can be accessed on most devices (phones/ipads/tablets) however, it is best viewed on a larger screen.
 Another similar resource that has even more examples with more indepth explanations over a larger range of sizes (from 10^{–}^{35} m to 10^{+27} m) can be found at The Scale of the Universe  and it was created by high school students! This could be a fun website to explore after completing this activity, and as all of the objects from the list in step 2 are specifically referenced in this program, it could be used for students to check their predictions.
 Students will continue to work in their small groups to answer questions using scientific notation and the interactive. After each group has answered questions 712, review the answers together as a class.
 For these questions at the end of the activity, students’ answers should be reported with positive exponents based on the way the questions are phrased. Something would be 10^{2} times (100 times) bigger or smaller, but you would never say something is 10^{–2} times (0.01 times) bigger or smaller. The direction of the comparison is indicated by the phrases “how many times bigger” vs. “how many times smaller” rather than the +/– sign of the exponent.
For the Student
Lesson
Guiding Questions
 If we could split a piece of gold into smaller and smaller pieces, how small could we get – and have it still be gold?
 How small is an atom, both qualitatively and quantitatively?
 How can I express the size of an atom of gold using scientific notation?
Instructions
 In small groups, discuss the guiding question, “How small is an atom?” Make a prediction, using meters as your units and write it on your whiteboard. For example, is an atom 1/10^{th} of a meter across? 1/1000^{th}? Etc.
 Also on your whiteboard, make 2 columns titled “larger than one gold atom” and “smaller than one gold atom.” With your group, discuss where each of the following items should be placed, and write your predictions in the corresponding column. (Don’t copy them onto your paper until you check your answers in step 5.)



 After your group has completed your prediction, go to the following website: http://micro.magnet.fsu.edu/primer/java/scienceopticsu/powersof10/index.html
 Allow the program to run through once, and then you can select “Manual.” Each picture is 10 times smaller than the picture that precedes it. The number in the bottom left corner provides the measurement in meters. The numbers are written in powers of 10, or scientific notation. Example: an individual leaf cell is 10^{–}^{5} meters across, while a leaf cell nucleus is 10 times smaller, or 10^{–}^{6} meters across.
 After exploring the program, work with your group to make any corrections to your estimated size of an atom and the “larger” and “smaller” predictions on your whiteboards. Copy your corrected answers below.
How small is an atom? ________________
Larger than one gold atom  Smaller than one gold atom 
 Use the powers of 10 program to help you answer the questions below. The first one is complete for you as an example.
Ex. How many times larger is the Milky Way galaxy than the earth?
In order to solve: Step 1: Manually move to the view of the Milky Way (10^{+21 }meters). Write this out longhand (1,000,000,000,000,000,000,000)
 Step 2: Manually move to the view of the Earth (10^{+7 }meters). Write this out longhand (10,000,000).
 Step 3: Count how many more zeroes are in the number for the Milky Way (14, so the Milky Way is 10^{+14} or 100,000,000,000,000 times bigger than earth)
 Alternate solution: You can also do this using division – just find the difference between the two exponents (10^{+21 }meters/10^{+7 }meters à the Milky Way galaxy is 10^{+14 }times larger than the Earth)
 How many times larger is an oak leaf than the nucleus of an oak leaf cell?
 How many times smaller is a carbon atom than an oak leaf?
 How many times smaller is a proton than a DNA nucleotide?
 How many times larger is the Milky Way than our solar system?
Challenge Questions
 Just how small is a gold atom? The diameter of an atom of gold is about 0.00000000027 meters. Write this out in scientific notation.
 If you have 6.02 x 10^{23} gold atoms, laid out in a row, how long would it be?