Subject Area(s) science & technology, number & operations, algebra Associated Unit

Associated Lesson

Activity Title Could “Muggles” Play Wizard Chess?

Header Image 1, [centered]

Grade Level 11 (9-12) Activity Dependency

Time Required 90 minutes (one 45 minute class period for nitinol activity and discussions, a second class period for discussion of homework and scientific notation worksheet)

Group Size 2

Expendable Cost per Group US$0 (Note: nitinol wire is not readily available in most classrooms, but once purchased, the wire can be used for many years) Summary The broad goal of this science activity is to expose students to shape memory alloys—nitinol (a class of nickel-titanium alloys) in particular—in order to discuss current research in materials science and engineering, to link interesting science phenomena to pop-culture via Harry Potter, and to encourage students to use internet resources to learn about science, technology, and

Image 1 ADA Description: close-up photograph of a carved chess piece (a white knight)

sitting on a chess board Caption: Could “muggles” play Wizard

Chess? Image file: sma_image1.jpg

Source/Rights: Copyright © Microsoft Corporation, One Microsoft Way,

Redmond, WA 98052-6399 USA. All rights reserved.

engineering. Because the mechanisms responsible for its memory properties act at the atomistic scale, some consider nitinol to be nanotechnology. Scientific notation is a convenient way to deal with very small (and very large) numbers, so practicing algebraic manipulations with numbers written in such form facilitates discussion of nanotechnology.

Engineering Connection Surprising physical phenomena occur at the nanoscale, and engineers have begun to use nanotechnology to address macroscale problems. Shape memory alloys (considered by some to be a nanotechnology) have properties that can be exploited to improve medical and orthodontic standards of care among numerous other practical applications. Because of the range of scales involved and the convenience it offers, engineers frequently scientific notation to express numbers.

Engineering Category = #1

Keywords Harry Potter, nanotechnology, nitinol, scientific notation, shape memory alloy

Educational Standards ITEEA, Standard 14, Grades 9-12, K. Medical technologies include prevention and

rehabilitation, vaccines and pharmaceuticals, medical and surgical procedures, genetic engineering, and the systems within which health is protected and maintained.

Texas Essential Knowledge and Skills (TEKS) §112.39. Physics, (c) (2) (F) “Scientific processes. …The student is expected to… demonstrate the use of course apparatus, equipment, techniques, and procedures, including… hot plates, …Celsius thermometers, …”

Pre-Requisite Knowledge

Familiarity with scientific notation and algebraic manipulations. Basic knowledge of the atomic nature of solids. Basic knowledge of electricity and magnetism.

Learning Objectives After this activity, students should be able to:

Observe shape memory alloy transition from deformed to “trained” state Describe shape memory alloy’s molecular structure Draw simplified models of shape memory alloy structure Discuss (potential) applications for shape memory alloys Express and manipulate numbers in scientific notation

Materials List Each group of two needs:

Nitinol wire (roughly 10cm long; initially crumpled, but “trained” to resume a different shape)

Thermometer Hot plate or Bunsen burner with ring stand Water (150-200mL) Beaker (250mL or larger) Tweezers

Each student needs: Eye protection (goggles or safety glasses) “Nitinol: A Smart Metal” handout “Scientific Notation Review and Practice” worksheet Calculator (a graphing calculator recommended because of ease of entering numbers for

computation, but a scientific calculator is sufficient) Note: nitinol wire can be purchased from Edmund Scientific; as of December 2011, they sell “Wire with a Memory” in 7.62cm (3 inch) lengths, two wires per pack; each pack is $9.00. Once purchased, the wire can be reused with many classes. (Link to product page:http://www.scientificsonline.com/wire-with-a-memory.html?&cm_mmc=Mercent-_-Google-_-NULL-_-3037308&mr:trackingCode=B06D1735-DB81-DE11-8C0A-000423C27502&mr:referralID=NA ).

Introduction / Motivation How many of you are familiar with Harry Potter and the Sorcerer’s Stone? Do you remember the scene where Harry, Ron and Hermione are forced to play a larger than life version of Wizard Chess? (Instructor plays scene from the movie; a free version (5:36 run time) with watermark is available on YouTube at http://www.youtube.com/watch?v=imiVDYfoh54&feature=related ).

Do you think that such a thing is science fiction or science fact? Actually, recent advances in materials science, nanotechnology, and electronics may make it possible for muggles (a Harry Potter term for non-magical people) to have this experience in real life. We will try to understand the fundamentals of this technology today, but first I’d like to introduce you to a very smart piece of wire with a long memory.

Vocabulary / Definitions

Word Definition

alloy A homogeneous material that is a mixture of a metal and one or more other chemical species (not necessarily metallic), wherein the atoms of one or more species either occupy interstitial spaces or replace atoms of the other

Medical technology

“Prevention and rehabilitation, vaccines and pharmaceuticals, medical and surgical procedures, genetic engineering, and the systems within which health is protected and maintained” (ITEEA, Standard 14, Grades 9-12, K).

muggle A term from Harry Potter used to describe non-magical people

nanotechnology Construction and manipulation of devices, materials, or features that are 1 to 100 nanometers (10-9 to 10-5 meters) in length (note: nanotechnology is a new and diverse research area; a more precise definition is still being formed by researchers)

shape memory alloys

An alloys that is able to return to a cold-forged shape from a deformed state after being heated or stressed.

Procedure Background

1. Shape memory alloys are known by many names: SMA, smart metal, memory metal, memory alloy, muscle wire, smart alloy. These descriptive names refer to the unique property of these alloys to return to a cold-forged shape from a deformed state after being heated or stressed. These materials hold promise to replace conventional hydraulic- and pneumatic-based actuators because SMAs have superior power-to-weight ratios.

2. Shape memory polymers and ferromagnetic memory alloys have also been developed that exhibit shape memory properties without use of metals or under application of strong magnetic fields, respectively.

3. Emerging technology that uses shape memory alloys is appearing across many fields: aircraft, dentistry, medicine, optometry, orthopedic surgery, piping, and robotics

4. SMAs are also used to make stents, a medical technology used to prevent stenosis (or narrowing) of vasculature in the body—especially in arteries. (ITEEA, Standard 14, Grades 9-12, K. Medical technologies include prevention and rehabilitation, vaccines and pharmaceuticals, medical and surgical procedures, genetic engineering, and the systems within which health is protected and maintained.) Since they want to return to their trained shape, nitinol stents tend to remain flush against the vessel wall. This is a major advantage over conventional stents which require a balloon to press the stent against the inside of the vessel.

5. A video of a nitinol stent deployment is available at http://www.youtube.com/watch?v=D8bx99ZA-eU&feature=related . The first part of the clip talks about problems on balloon inflated stents, but at 1:36 the topic changes to a discussion of the Stentys nitinol stent. Unfortunately the video uses a lot of medical jargon, but the key ideas about the technology can be grasped.

6. Because of the crucial importance that nanosized features have on SMA functionality, some researchers classify SMAs as a nanotechnology. Nanotechnology, however, is a very diverse field and a single definition (that satisfies all researchers who claim to be nanotechnologists) is yet to be found. Nevertheless, we can consider nanotechnology to refer to construction and manipulation of devices, materials, or features that are 1 to 100 nanometers (10-9 to 10-5 meters) in length.

7. Though more frequently encountered in materials science and electrical engineering research laboratories, nanotechnology can be found in everyday life. Some familiar products that may contain nanoparticles are:

car paints (particles enhance shine, water repellence, and durability) sunscreen and make-up (particles better reflect damaging light) hair-styling flat-irons (particles give greater smoothness, more even heat distribution

and durability) golf balls (particles reduce spin, thus straightening the flight path) cancer treatment (particles eliminate tumors without traditional radiation)

8. Companies are rushing to bring even more products to the marketplace. Nanotechnology is helpful in medicine, where doctors are hoping that the effectiveness of pharmaceuticals and the sensitivity of sensors can be increased. (Nano-sized wires and circuits will further reduce the size of electronic devices and improve digital displays. Stronger and lighter materials are being developed by examining their nano-scale structure. The applications of using these very small materials are presently being explored tremendously, from electronics, medicine, energy efficiency, material science and so much more, with the basic purpose of improving our lives,

improving what devices and technology that now exist. Learning about how to deal with these small particles starts with learning how to deal with the numbers that their applications use.

9. Scientific (or exponential) notation is a short-hand way to express and compare very large and very small numbers compactly and quickly. To be in proper form, a number in scientific notation has the form , where a (called the significand) is a real number whose absolute value is greater than or equal to 1 but is less than 10 and b is an integer (it can be positive, negative, or zero).

10. When scientific notation is used to express measurements (like length and mass), special prefixes can be added to the unit of measure instead of writing “x10b “. For example, 1.25x103 meters can be written as 1.25 kilometers, since kilo means 10³ or 1,000. Common prefixes and the “powers of ten” they correspond to are given below.

small (less than 1 unit) LARGE (GREATER THAN 1 UNIT)

deci (d)

10-1

DECA (da)

10 1

centi (c)

10-2

HEPTO (h)

10 2

milli (m)

10-3

KILO (k)

10 3

micro (μ)

10-6

MEGA (M)

10 6

nano (n)

10-9

GIGA (G)

10 9

pico (p)

10-12

TERA (T)

10 12

femto (f)

10-15

PETA (P)

10 15

atto (a)

10-18

EXA (E)

10 18

zepto (z)

10-21

ZETTA (Z)

10 21

yacto (y)

10-24

YOTTA (Y)

10 24

11. Operations with numbers written in scientific notation: a. To add or subtract, first make sure each number is expressed in terms of the same

power of ten—this may require shifting the decimal left or right so that one (or more) of the numbers is no longer in proper form. Once the powers are equal, the significands can be operated on normally, while the powers of ten are carried along. When all numbers have been summed or differenced, the final result can be put back into proper form.

b. To multiply, multiply the significands, add the powers of ten, and adjust the result back into proper notation

c. To divide, divide the significands, subtract the divisor’s power of ten from the dividend’s, and adjust the result back into proper notation

d. To exponentiate, raise significand to the given power, multiply the power of ten by the exponent value, and adjust the result back into proper notation

Before the Activity Gather materials, pair students for the activity, and distribute materials and “Nitinol: A Smart Metal” handout.

With the Students

Day One 1. Motivate lesson by playing a clip of Wizard Chess from Harry Potter and the Sorcerer’s Stone

and asking the students whether this is science fiction or science fact. (a free version (5:36 run time) with watermark is available on YouTube at http://www.youtube.com/watch?v=imiVDYfoh54&feature=related)

2. Ask students to continue to think about the reality of wizard chess while doing the activity 3. Instruct the students how to use the hot plate safely and how to read the thermometer (Texas

Essential Knowledge and Skills (TEKS) §112.39. Physics,… (c) (2) (F) “Scientific processes. …The student is expected to… demonstrate the use of course apparatus, equipment, techniques, and procedures, including… hot plates, …Celsius thermometers, …)

4. Students follow the steps listed on the “Nitinol: A Smart Metal” handout a. Students fill their beakers with water b. Students allow water to heat on a hot plate until water reaches roughly 50-90˚C

(this temperature depends on the specific alloy of nitinol used) c. Students turn off heating on hot pate (to ensure water does not boil) d. Students dip the nitinol wire in hot water e. Students observe and record the results f. Students may allow wire to cool, crumple it, and repeat steps a through e

5. Students put away materials 6. Class discusses observations 7. Instructor shares information about how the transition is achieved molecularly

a. discussion of alloys—ask students what an alloy is, for some examples of alloys, and what the purpose of alloying is

i. alloy definition 1. draw interstitial alloy: 2. draw substitutional alloy:

Image 2, [left justified]

Image 3, [right justified]

Image 2 ADA Description: a schematic showing a regular array of large circles

with smaller circles distributed unevenly in the gaps Caption: An interstitial alloy is one in which atoms of a second element

are incorporated by filling in between atoms of the first element Image file: sma_image2.png

Source/Rights: Copyright © John Aplessed, Wikimedia Commons, http://en.wikipedia.org/wiki/File:Alloy_Interstitial.svg

Image 3 ADA Description: a schematic showing a regular array of circles most are colored red, but a few of the circles (seemingly at random) are blue

Caption: A substitutional alloy is one in which atoms of a second element are incorporated by replacing atoms of the first element

Image file: sma_image3.png Source/Rights: Copyright © John Aplessed, Wikimedia Commons,

http://en.wikipedia.org/wiki/File:Alloy_Substitutional.svg

ii. familiar alloy examples: steel, bronze, brass, jewelry gold iii. purpose: obtain material properties different from those of a material made

entirely of any single element b. discussion of nitinol, in particular

i. Nitinol is a SMA made from careful combination of nickel and titanium. ii. Unlike most alloys, the atoms in SMAs are able to move reversibly from

one crystal state to another. (Wikipedia “A reversible transformation does not involve this diffusion of atoms, instead all the atoms shift at the same time to form a new structure, much in the way a parallelogram can be made out of a square by pushing on two opposing sides”)

iii. atoms in nitinol transition from austenitic to martensitic structures 1. austenite: simple cubic unit cell 2. martensite: parallelepiped unit cell

8. Instructor models of transition a. draws atoms in lattice

Image 4, [centered]

Image 5, [centered]

Image 4 ADA Description: Simplistic lattice

models of martensite (left side of image) and austenite (right side of image). In

martensite, nickel and titanium atoms are arranged at the corners of a

parallelepiped. In austenite, titanium atoms are arranged at the corners of

perfect cubes, while nickel atoms are in the center of the cubes.

Caption: Schematic representations of the martensite and austenite lattices

Image file: sma_image4.gif Source/Rights: Copyright © 2008 The Board of Regents of the University of

Wisconsin System. http://mrsec.wisc.edu/Edetc/background/

memmetal/index.html Copyright permission not yet obtained

Image 5 ADA Description: Simplistic lattice models of

martensite (left side of image) and austenite (right side of image). In martensite, nickel and titanium

atoms are arranged at the corners of a parallelepiped. In austenite, titanium atoms are arranged at the corners of perfect cubes, while

nickel atoms are in the center of the cubes. Caption: Schematic representations of the

martensite and austenite lattices with atomic spacings given

Image file: sma_image5.jpg Source/Rights: Copyright © Tom Duerig,

Wikimedia Commons, http://en.wikipedia.org/wiki/File:Nitinol_Austenite_

and_martensite.jpg al.svg

b. shows (or passes around the room) a ball-and-stick molecular model, if available 9. Explain how Wizards’ Chess could be played with advanced electromagnetics and SMAs

a. changing magnetic field could move pieces from square to square b. carbon nanotube wires could handle large currents to make generation of

magnetic fields more efficient c. SMA to change shape of pieces d. electrical arcing or ultrasonics could be used to blast pieces

10. Ask students for their opinions on how SMAs could be used in everyday life 11. Give examples of uses of SMAs in everyday life

a. aircraft b. stents c. orthodontics—braces

Day Two

1. Recap lesson from Day One 2. Ask students to share their homework findings; write SMAs compositions and

applications on the board 3. Call students attention to the fact that the interesting features of SMAs are due to changes

at the atomic length-scale 4. Define nanotechnology 5. Remind students of what scientific notation is and how it’s useful 6. Go over first page of “Scientific Notation Review and Practice” worksheet

a. discuss “proper form” b. discuss operations and example calculations c. if students seem confused or uncertain, perform additional examples

7. Have students solve the problems on the second page of “Scientific Notation Review and Practice” worksheet

a. students may work alone or in small groups b. students may finish the worksheet during class or take it home as homework

Attachments “Nitinol: A Smart Metal” handout (docx)

“Nitinol: A Smart Metal” handout (pdf)

“Scientific Notation Review and Practice” worksheet (docx)

“Scientific Notation Review and Practice” worksheet (pdf)

“Scientific Notation Review and Practice” worksheet answers (docx)

“Scientific Notation Review and Practice” worksheet answers (pdf)

Safety Issues Use eye protection (goggles or safety glasses) during this activity Use caution near the heat source and when handling hot beakers, water, and wires

Troubleshooting Tips If the wire “resists” being bent or shaped, it is possible that the wire’s temperature is still above or

near the transition temperature; try dipping the segment into a beaker of ice water.

If the wire “resists” returning to its “trained” shape, it is possible that the wire’s temperature is not high enough; try increasing the water temperature or carefully passing the wire through a flame.

Investigating Questions

Assessment

Pre-Activity Assessment Baseline

Ask students is they have ever heard of SMAs Ask students if they think Wizard Chess is possible Ask students whether it is possible to teach a metal to do something

Activity Embedded Assessment Observe

Students deform and restore the shape of nitinol wires

Post-Activity Assessment SMA Homework Assignment (included on “Nitinol: A Smart Metal” handout)

write one paragraph describing why the nitinol wire behaves in the manner observed in class

find the name or composition of one (or more) shape memory alloy(s) write two paragraphs describing technology that uses shape memory alloys (students

given potential areas to explore: aircraft, dentistry, medicine, optometry, orthopedic surgery, piping, and robotics); include

o alloy composition o detailed description of application o advantage of SMA in this application

Scientific Notation Review and Practice Worksheet complete the worksheet worksheet can be done in class, at home, or started at school and finished for homework

Activity Extensions

Activity Scaling For lower grades, the scientific notation worksheet could be omitted and discussion of the SMAs could be kept at a more superficial level by eschewing detailed discussion of the SMA atomic structure.

Additional Multimedia Support A clip of Wizard Chess from Harry Potter and the Sorcerer’s Stone (a free version (5:36 run

time) with watermark is available at http://www.youtube.com/watch?v=imiVDYfoh54&feature=related) Last accessed 15 December 2011.

A video of a nitinol stent is available at http://www.youtube.com/watch?v=D8bx99ZA-eU&feature=related . The first part of the clip talks about problems on balloon inflated stents, but at 1:36 the topic changes to a discussion of the Stentys SMA stent. Unfortunately the video uses

a lot of medical jargon, but the key ideas about the technology can be grasped. Last accessed 15 December 2011.

References Alloy. Last modified 14 December 2011. Wikipedia. Accessed 15 December 2011.

http://en.wikipedia.org/wiki/Alloy (some background discussion)

Nitinol. Last modified 8 December 2011. Wikipedia. Accessed 15 December 2011. http://en.wikipedia.org/wiki/Nitinol (some background discussion)

Exploring the Nano World: Memory Metal. Last modified 2008. Materials Research Science and Engineering Center at the University of Wisconsin, Madison. Accessed 15 December 2011. http://mrsec.wisc.edu/Edetc/background/memmetal/index.html

Kauffman, George, and Isaac Mayo. "Memory Metal." Chem Matters. Oct. (1993): 4-7.

Other

Redirect URL

Contributors Holley Love, Roberto Dimaliwat

Copyright

Supporting Program National Science Foundation AWARD # 0840889—New, GK-12 Program at the University of Houston: Innovations in Nanotechnology and Nanosciences using a Knowledge, Applications, Research, and Technology (KART) Approach—Pradeep Sharma, Ph.D., Principal Investigator

NITINOL: A SMART METAL

alloy: a metallic material made from two or more chemical elements, at least one of which is a metal

shape memory alloy: a blend of metals that has the ability to transform from a deformed state to a “learned” cold-forged state upon application of heat or stress

nitinol: a shape memory alloy composed of nickel and titanium where the nickel represents 55-56 weight-percent of the final alloy

Because of their ability to return to an original shape when heated or stressed, shape memory alloys (SMAs) are frequently called smart metals, memory metals, memory alloys, muscle wires, or smart alloys. SMAs are finding uses in many industries and clinics because of their shape memory properties. Though “memory” is a convenient descriptive term, the return to the original shape occurs because heat (or sometimes externally applied stress) allows the atoms in the alloy to move into a more favorable orientation. ACTIVITY:

1. Form groups of two or three and collect the following materials a. Nitinol wire (initially crumpled, but “trained” to resume a different shape) b. Thermometer c. Hot plate d. Water (150-200mL) e. Beaker (250mL or larger)

2. Fill the beaker with 150-200mL of water 3. Allow the water to heat on the hot plate until the water reaches roughly 50-90˚C

(this temperature depends on the specific alloy of nitinol used) 4. Turn off heating on hot pate (to ensure water does not boil—high temperatures

may damage the wire) 5. Dip the nitinol wire in hot water 6. Observe and record the results 7. Allow wire to cool, re-crumple it, and repeat the steps above

HOMEWORK: 1. Write one paragraph describing why the nitinol wire behaves in the manner observed

during class. 2. Find the name or composition of one (or more) shape memory alloy(s). 3. write two paragraphs describing technology that uses shape memory alloys (students

given potential areas to explore: aircraft, dentistry, medicine, optometry, orthopedic surgery, piping, and robotics); include

alloy composition detailed description of application advantage of SMA in this application

Name _________________________________________________Date_________________________

SCIENTIFIC NOTATION REVIEW AND PRACTICE

Scientific (or exponential) notation is a short-hand way to express and compare very large and very small numbers

compactly and quickly. To be in proper form, a number in scientific notation has the form

,

where a (called the significand) is a real number whose absolute value is greater than or equal to 1 but is less than 10 and b

is an integer (it can be positive, negative, or zero). When scientific notation is used to express measurements (like length

and mass), special prefixes can be added to the unit of measure instead of writing “x10b

“. For example, 1.25x103 meters

can be written as 1.25 kilometers, since kilo means 10³ or 1,000. Common prefixes and the “powers of ten” they

correspond to are given below.

Small

deci (d)

centi (c)

milli (m)

micro (μ)

nano (n)

pico (p)

femto (f)

atto (a)

zepto (z)

yacto (y)

(less than 1 unit)

10-1

10-2

10-3

10-6

10-9

10-12

10-15

10-18

10-21

10-24

LARGE

DECA (da)

HEPTO (h)

KILO (k)

MEGA (M)

GIGA (G)

TERA (T)

PETA (P)

EXA (E)

ZETTA (Z)

YOTTA (Y)

(GREATER THAN 1 UNIT)

101

102

103

106

109

1012

1015

1018

1021

1024

To add or subtract numbers written in scientific notation, first make sure each number is expressed in terms of the same

power of ten—this may require shifting the decimal left or right so that one (or more) of the numbers is no longer in proper

form. Once the powers are equal, the significands can be operated on normally, while the powers of ten are carried along.

When all numbers have been summed or differenced, the final result can be put back into proper form.

EXAMPLE: Add 2.36x1025

, 3.25x1026

, and -7.00x1025

. 1) Adjust the decimal location so that all powers of ten are the same. Since two of the three are written as 10

25,

this is a convenient power to work with. The numbers become: 2.36x1025

, 32.5x1025

, and -7.00x1025

. 2) Perform the addition and subtraction, carrying along powers of ten:

(2.36x1025

+32.5x1025

)-7.00x1025

= (2.36+32.5-7.00)x1025

= 27.86x1025

. 3) Shift the result back into proper form: 27.86x10

25 = 2.786x10

26.

To multiply numbers written in scientific notation, multiply the significands, add the powers of ten, and adjust the result back into proper notation EXAMPLE: Find the product of -4.8x10

-3 and -9.1x10

3.

1) Multiply the significands: (-4.8x10-3

)x(-9.1x103) = (-4.8x-9.1)x10

-3x10

3 = 43.68 x10

-3x10

3.

2) Add the powers of ten: 43.68 x10-3

x103

= 43.68x10(-3+3)

= 43.68x100.

3) Shift the result back into proper form: 43.68x100

= 4.368x101.

To divide numbers written in scientific notation, divide the significands, subtract the divisor’s power of ten from the dividend’s, and adjust the result back into proper notation EXAMPLE: Evaluate 3.5x10

14/5x10

-3.

1) Divide the significands:

.

2) Subtract the divisor’s exponent from the dividend’s exponent:

.

3) Shift the result back into proper form: . To exponentiate numbers written in scientific notation, raise significand to the given power, multiply the power of ten by the exponent value, and adjust the result back into proper notation EXAMPLE: What is 2x10

3 raised to the 9

th power?

1) Exponentiate the significand: (2x103)

9 = 2

9x(10

3)

9 = 512x(10

3)

9.

2) Multiply the power of ten by the exponent value: 512x103x9

= 512x1027

. 3) Shift the result back into proper form: 512x10

27 = 5.12x10

29.

Practice:

1. Ultraviolet (UV) light is electromagnetic radiation that is damaging to living cells and can fade dyes and

pigments used in house paint, car paint, fabric, and paper goods. The wavelength of UV light ranges from 10

to 400 nanometers. Express this range in

a. meters

b. inches (1meter is about 39.37inches)

2. What are the volumes (expressed in cubic meters) of a cylindrical wire 1 centimeter long and

a. 1 millimeter in diameter?

b. 10 nanometers in diameter?

3. If the density of copper is 8.94x106 grams per cubic meter, what is the mass of each wire in Question 2?

4. If a single molecule of copper has a mass of 1.055x10-25 kilograms, how many molecules are present in each wire in Question 3?

5. Avogadro’s number (the number of molecules in one mole of substance) is 6.022x1023 molecules. How many moles are present in each wire in Question4?

6. A light year is used to measure large distances and represents the distance that light can travel in a year through the vacuum of space. If the speed of light is 3x108 meters per second, how far is a light year?

7. Proxima Centauri is the closest star to our sun at just 39,900,000,000,000 km away.

a. How far is this in meters using proper scientific notation?

b. What prefix (see table on the preceding page) would be more appropriate than “kilo”?

c. Using Question 6, how many light years is this?

8. The mass of the Earth is estimated to be 5.9736×1024 kg, and the mass of the sun is 1.98892×1030 kilograms. How many times larger is the sun’s mass than Earth’s?

9. The diameter of the moon is 3474.8 kilometers, whereas the diameter of the Earth is 12.7562 megameters.

What is

a. the sum of these diameters in meters?

b. the difference of these diameters in kilometers?

10. A nanotube has a diameter of about 4 nm, while human hair has a diameter of 40µm and a human wrist 40mm

a. how many nanotubes can you fit in a human hair? b. In a human wrist? c. The radius of the Earth is 6,378.1 km. How many nanotubes can fill the earth’s diameter?

SCIENTIFIC NOTATION REVIEW AND PRACTICE

ANSWERS

Please note the I have tried to produce accurate solutions to all problems, but there may be

computational errors; for these, I sincerely apologize. HCLove

1. Ultraviolet (UV) light is electromagnetic radiation that is damaging to living cells and can fade dyes

and pigments used in house paint, car paint, fabric, and paper goods. The wavelength of UV light

ranges from 10 to 400 nanometers. Express this range in

a. meters 1x10-8 to 4x10-7 meters

b. inches (1meter is about 39.37inches) 3.937x10-7 to 1.5748x10-5 inches

2. What are the volumes (expressed in cubic meters) of a cylindrical wire 1 centimeter long and

volume of a right circular cylinder= π *r2*L= π *(D2/4)*L

a. 1 millimeter in diameter? 7.85x10-9 [m3]

b. 10 nanometers in diameter? 7.85x10-19 [m3]

3. If the density of copper is 8.94x106 grams per cubic meter, what is the mass of each wire in Question 2? mass = density * volume

a. 1 millimeter in diameter? 7.02x10-2 [g]

b. 10 nanometers in diameter? 7.02x10-12 [g]

4. If a single molecule of copper has a mass of 1.055x10-25 kilograms, how many molecules are present in each wire in Question 3? total molecules = total mass / mass of single molecule

a. 1 millimeter in diameter? 6.66x1023 [molecules]

b. 10 nanometers in diameter? 6.66x1013 [molecules]

5. Avogadro’s number (the number of molecules in one mole of substance) is 6.022x1023 molecules. How many moles are present in each wire in Question4? moles = total molecules / Avogadro’s number

a. 1 millimeter in diameter? 1.10x100 [moles]

b. 10 nanometers in diameter? 1.10x10-10 [moles]

6. A light year is used to measure large distances and represents the distance that light can travel in a year through the vacuum of space. If the speed of light is 3x108 meters per second, how far is a light year?

meters per year= meters per second *seconds per minute*minutes per hour*hours per day*days per year = 3x10

8 *60 *60 *24 *365.25

9.47x1015 [m]

7. Proxima Centauri is the closest star to our sun at just 39,900,000,000,000 km away.

a. How far is this in meters using proper scientific notation? 3.99x1016 [m]

b. What prefix (see table on the preceding page) would be more appropriate than “kilo”? peta

c. Using Question 6, how many light years is this? 4.21 [lightyears]

8. The mass of the Earth is estimated to be 5.9736×1024 kg, and the mass of the sun is 1.98892×1030 kilograms. How many times larger is the sun’s mass than Earth’s? 3.33x105 times larger

9. The diameter of the moon is 3474.8 kilometers, whereas the diameter of the Earth is 12.7562

megameters. What is

a. the sum of these diameters in meters? 1.6231x107 [m]

b. the difference of these diameters in kilometers? 9.2814x103 [km]

10. A nanotube has a diameter of about 4 nm, while human hair has a diameter of 40µm and a human wrist 40mm

a. how many nanotubes can you fit in a human hair? 1x104 b. In a human wrist? 1x107 c. The radius of the Earth is 6,378.1 km. How many nanotubes can fill the earth’s diameter?

1.59x1015