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Notre Dame extended Research Community

Scale and Orders of Magnitude

Michael CrockerValerie GossRebecca Quardokus

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What do we mean by Scale?

A Few Small Mammals

Squirrel0.5kg

Cat7kg

8kg

Ferret2kg

Raccoon5kg

4kg0kg 6kg2kg

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What do we mean by Scale?A Few Whales

Killer6,000kg

Beluga1,000kg

10,000kg

Minke10,000kg

Pygmy Right3,000kg

5,000kg0kg 7,500kg2,500kg

Squirrel, Ferret, Raccoon, Cat (<10kg)

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How does this related to Nano?

Different Lengths

Giraffe5m

8m

Tree8m

Human2m

4m0m 6m2m

Transistors, Molecules, Atoms, etc.

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Orders of Magnitude Powers of Ten

Billionths = 0.000 000 001 = 10-9 Nano Millionths = 0.000 001 = 10-6

Micro Thousandths = 0.001 = 10-3

Milli Hundredths= 0.01 = 10-2

Tenths = 0.1 = 10-1

Ones = 1 = 100

Tens = 10 = 101

Hundreds = 100 = 102

Thousands = 1,000 = 103 Kilo Millions = 1,000,000 = 106

Mega Billions = 1,000,000,000 = 109 Giga

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Exponent - 103

Billionths = Nano = 10-9

Millionths = Micro = 10-6

Thousandths = Milli = 10-3

Ones = Base Unit = 100

Thousands = Kilo = 103

Millions = Mega = 106

Billions = Giga = 109

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Prefixes with “Meter” – Steps of 1,000

Meter

Kilometer

Megameter

Millimeter

Micrometer

Nanometer

100

103

106

10-3

10-6

10-9

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Scale Calculations

1. Let’s first look at common items that can be measured on about the same scale

2. Then let’s look at well known items that are not on the same scale

3. Finally, let’s look at nanostructures that are definitely not on the same scale as our day-to-day experiences

Brick vs. Human

Brick vs. Egyptian Pyramid

Brick vs. Nanomagnet

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Brick

~50mm

~200mm

~100mm

Volume:50mm * 100mm * 200mm

1,000,000 mm3

10-3 m3

Mass:

2 kg

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Human

Volume:2000mm * 300mm * 200mm

100,000,000 mm3

10-1 m3

Mass:

100 kg

~2m

~30cm

~20cm

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Compare – Human to Brick

vs.

100kg10-1 m3

2kg10-3 m3

50 times the mass100 times the

volume½ the density

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Egyptian Pyramid

5 billion kg (5*109), 2.5 million m3

(2.5*106)

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Compare – Brick to Pyramid

vs.

2 kg, 10-3

m3

5*109 kg, 2.5*106

m3

2.5*109 times the mass2.5*109 times the

volumeAbout the same the density

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Nano-Electronics

Transistors - Micrometers

Nanomagnets - Nanometers

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Nano-Electronics Zoomed In

Transistors - Micrometers

Nanomagnets - Nanometers

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Compare – Nanomagnet to Brick

vs.

1.4*10-18 kg, 1.6*10-22

m32 kg, 10-3

m3

1.43*1018 times the mass6.25*1018 times the

volumeAbout ¼ the density

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Nanomagnets Across a Brick

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Time for a Game!

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Fold/Cut Paper

How many times can you fold a piece of paper in half?

How many times can you cut a piece of paper in half?

What do these exercises illustrate?

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Scale Bar

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“Well Spaced” Objects for Game

Atom10-27

Cell10-15

Bee10-5

Elephant103

Skyscraper108

Mountain1015

Moon1022

Sun1030