**STUDY MATERIAL, TEMPLATE, SAMPLE PROBLEMS AND INSTRUCTIONS ATTACHED BELOW**

- Consider two stable isotopes, helium-3 and helium-4. How many neutrons and protons are there in each isotope? What are the mass numbers? Hint: Do not confuse mass number with atomic mass. Review the definition of them.
- There are two water containers: a cube and a sphere. The length of the side of the cube is 3 m and the radius of the sphere is 3 m. When the two containers are full of water, which container contains more mass? Hint: Use the relationship between density, mass, and volume. Mass=density x volume. If the length of the side of a cube is r m, the volume of the cube is r3 m3.

A slingshot has a spring constant of 50 N/m. If you apply a force of 10 N, how far does it stretch? Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx, where k is the spring constant and x is the displacement of the spring from its original length.

2.If two protons and two neutrons are added to the nucleus of a carbon atom, what nucleus does it become? Hint: The proton number equals to the atomic number. See the periodic table of Figure 11.9 on. p. 216 in the textbook.

3.Calculate the molecular mass of hydrogen sulfide, H2S in atomic mass unit u. Use the periodic table of Figure 11.9 on. p. 216 in the textbook. Hint: The molecular mass of a molecule is the sum of the atomic masses of its atoms. For instance, hydrogen and oxygen have atomic masses of 1.0079u and 15.999u respectively (See Figure 11.9 on. page 216 in the textbook). Thus, the molecular mass of a water molecule (H2O) is (2×1.0079u+15.999u=18.0148u). In order to express enormous numbers of atoms or molecules, the gram-mole, or, more simply, the mole, is used.

4.Which has the greater density: 100 kg of ice or 10 kg of gold? Consult the Table 12.1 on p. 230 in the textbook. Hint: Be careful about the unit of density, mass, and volume.

5.What is the volume of 1,000 kg of ice? Consult the Table 12.1 on p. 230 in the textbook. Hint: Use the relationship between density, mass, and volume. Mass=density x volume.

6.How many gold atoms are in a 1 kg gold bar? The chemical symbol of gold is Au. Consult

The Periodic Table in Figure 11.9 on p. 216 in the textbook. Hint: Remember 1u=1.66×10-27kg.1 mole= 6.022×1023, which is Avogadro’s number

If the radius of a sphere is r, the volume of the sphere is 4/3 xπ x r3 m3. Here x r3 =r x r x r.

8.A force of 100 N is required to squeeze a hand exerciser that has a coiled spring. The spring is compressed by 0.02 meters. Determine the spring constant. Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx, where k is the spring constant and x is the displacement of the spring from its original length.

A spring has a spring constant of 300 N/m. Find the magnitude of the force needed to compress the spring by 0.03 m. Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx, where k is the spring constant and x is the displacement of the spring from its

- Consider two stable isotopes, helium-3 and helium-4. How many neutrons and protons are there in each isotope? What are the mass numbers? Hint: Do not confuse mass number with atomic mass. Review the definition of them.

There are two water containers: a cube and a sphere. The length of the side of the cube is 3 m and the radius of the sphere is 3 m. When the two containers are full of water, which container contains more mass? Hint: Use the relationship between density, mass, and volume. Mass=density x volume. If the length of the side of a cube is r m, the volume of the cube is r3 m3.A slingshot has a spring constant of 50 N/m. If you apply a force of 10 N, how far does it stretch? Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx, where k is the spring constant and x is the displacement of the spring from its original length.

2.If two protons and two neutrons are added to the nucleus of a carbon atom, what nucleus does it become? Hint: The proton number equals to the atomic number. See the periodic table of Figure 11.9 on. p. 216 in the textbook.

3.Calculate the molecular mass of hydrogen sulfide, H2S in atomic mass unit u. Use the periodic table of Figure 11.9 on. p. 216 in the textbook. Hint: The molecular mass of a molecule is the sum of the atomic masses of its atoms. For instance, hydrogen and oxygen have atomic masses of 1.0079u and 15.999u respectively (See Figure 11.9 on. page 216 in the textbook). Thus, the molecular mass of a water molecule (H2O) is (2×1.0079u+15.999u=18.0148u). In order to express enormous numbers of atoms or molecules, the gram-mole, or, more simply, the mole, is used.

4.Which has the greater density: 100 kg of ice or 10 kg of gold? Consult the Table 12.1 on p. 230 in the textbook. Hint: Be careful about the unit of density, mass, and volume.

5.What is the volume of 1,000 kg of ice? Consult the Table 12.1 on p. 230 in the textbook. Hint: Use the relationship between density, mass, and volume. Mass=density x volume.

6.How many gold atoms are in a 1 kg gold bar? The chemical symbol of gold is Au. Consult

The Periodic Table in Figure 11.9 on p. 216 in the textbook. Hint: Remember 1u=1.66×10-27kg.1 mole= 6.022×1023, which is Avogadro’s numberIf the radius of a sphere is r, the volume of the sphere is 4/3 xπ x r3 m3. Here x r3 =r x r x r.

8.A force of 100 N is required to squeeze a hand exerciser that has a coiled spring. The spring is compressed by 0.02 meters. Determine the spring constant. Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx, where k is the spring constant and x is the displacement of the spring from its original length.

A spring has a spring constant of 300 N/m. Find the magnitude of the force needed to compress the spring by 0.03 m. Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx, where k is the spring constant and x is the displacement of the spring from its

UNIT 5 INSTRUCTIONS

We have reviewed many important characteristics of moving objects in a gravitational field in Unit IV. In the previous

units, we considered many physical concepts in a macroscopic view. In this unit, we will investigate the fundamental

structure of matter with the composition on a smaller scale. In Unit V, we will review the basic chemical and physical

properties of the atomic structure. We will review how the organization of elementary particles such as protons,

neutrons, and electrons is the main factor to determine the identity of a material. We will analyze the Periodic Table

thoroughly because it contains integrated information regarding atomic structure. In addition, we will review the

motion of elementary particles with various atomic models.

For the Unit V Assignment, there will be 10 questions in Problem Solving. However, you only need to select 8

questions and must show the intermediate steps before you arrive at your answer. Before doing this, I highly

recommend that you thoroughly review the unit lesson and the three examples with solutions in the Study Guide.

Instructions

For this assignment, you will complete the Unit V problem solving practice assignment

worksheet. This assignment will allow you to demonstrate what you have learned in this unit.

Instructions for completing this assignment are located on the worksheet.

Save all of your work directly to the template.

Unit V Problem Solving Worksheet

This assignment will allow you to demonstrate the following objectives:

•

Identify the building blocks of matter to include their influence on physical properties.

o Identify the atomic mass and number of atoms in elements by utilizing the periodic table.

o Find the relation between mass, density, and volume.

o Distinguish applied force, spring constant, and displacement using Hooke’s law.

Instructions: Choose 8 of the 10 problems below. Show your work in detail. Answer the questions directly

in this template. Before doing this, it is highly recommending that you thoroughly review the three examples

in the Unit Lesson.

1. Consider two stable isotopes, helium-3 and helium-4. How many neutrons and protons are there

in each isotope? What are the mass numbers? Hint: Do not confuse mass number with atomic

mass. Review the definition of them.

2. If two protons and two neutrons are added to the nucleus of a carbon atom, what nucleus does it

become? Hint: The proton number equals to the atomic number. See the periodic table of Figure

11.9 on. p. 216 in the textbook.

3. Calculate the molecular mass of hydrogen sulfide, H2S in atomic mass unit u. Use the periodic

table of Figure 11.9 on. p. 216 in the textbook. Hint: The molecular mass of a molecule is the sum

of the atomic masses of its atoms. For instance, hydrogen and oxygen have atomic masses of

1.0079u and 15.999u respectively (See Figure 11.9 on. page 216 in the textbook). Thus, the

molecular mass of a water molecule (H2O) is (2×1.0079u+15.999u=18.0148u). In order to

express enormous numbers of atoms or molecules, the gram-mole, or, more simply, the mole, is

used.

4. Which has the greater density: 100 kg of ice or 10 kg of gold? Consult the Table 12.1 on p. 230 in

the textbook. Hint: Be careful about the unit of density, mass, and volume.

5. What is the volume of 1,000 kg of ice? Consult the Table 12.1 on p. 230 in the textbook. Hint:

Use the relationship between density, mass, and volume. Mass=density x volume.

6. How many gold atoms are in a 1 kg gold bar? The chemical symbol of gold is Au. Consult

The Periodic Table in Figure 11.9 on p. 216 in the textbook. Hint: Remember 1u=1.66×10-27kg. 1

mole= 6.022×1023, which is Avogadro’s number

7. There are two water containers: a cube and a sphere. The length of the side of the cube is 3 m

and the radius of the sphere is 3 m. When the two containers are full of water, which container

contains more mass? Hint: Use the relationship between density, mass, and volume.

Mass=density x volume. If the length of the side of a cube is r m, the volume of the cube is r3 m3.

If the radius of a sphere is r, the volume of the sphere is 4/3 xπ x r3 m3. Here x r3 =r x r x r.

8. A force of 100 N is required to squeeze a hand exerciser that has a coiled spring. The spring is

compressed by 0.02 meters. Determine the spring constant. Hint: Use Hooke’s law. The restoring

force of an ideal spring is F=-kx, where k is the spring constant and x is the displacement of the

spring from its original length.

Unit V Problem Solving Worksheet

9.

A slingshot has a spring constant of 50 N/m. If you apply a force of 10 N, how far does it stretch?

Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx, where k is the spring constant

and x is the displacement of the spring from its original length.

10.

A spring has a spring constant of 300 N/m. Find the magnitude of the force needed to compress

the spring by 0.03 m. Hint: Use Hooke’s law. The restoring force of an ideal spring is F=-kx, where

k is the spring constant and x is the displacement of the spring from its original length.

UNIT V STUDY GUIDE

Properties of Matter I

Course Learning Outcomes for Unit V

Upon completion of this unit, students should be able to:

5. Identify the building blocks of matter to include their influence on physical properties.

5.1 Identify the atomic mass and number of atoms in elements by utilizing the periodic table.

5.2 Find the relation among mass, density, and volume.

5.3 Distinguish applied force, spring constant, and displacement using Hooke’s law.

Reading Assignment

Chapter 11: The Atomic Nature of Matter

Chapter 12: Solids

Unit Lesson

What is the most fundamental particle?

The question about the most basic building blocks

of matter has a very long history. Most ancient

Greek philosophers believed that the fundamental

elements are water, earth, fire and air. In fact,

Democritus (460-370 B.C.) proposed that matter

is composed of atoms and thought that different

matter contains a different combination of atoms;

however, his idea did not attract the public’s

interest until Dalton (1766–1844) established the

theory of atoms. A more sophisticated atomic

model was developed by Rutherford (1871–1937)

and Bohr (1885–1962) (“Early atomic

understanding, n.d.; “The Atomic Model, n.d.).

The atom consists of a nucleus and electrons. A

nucleus is in the center of the atom, and electrons

All things in nature are made of atoms.

surround the nucleus with a relatively large

distance (~10-10m) from the nucleus. The size of

-15

the nucleus is about 10 m. The nucleus contains protons and neutrons. Electrons have a negative charge,

protons have a positive charge, and neutrons have no charge; they are neutral. In the natural state, an atom

is neutral because the number of protons is equal to the number of electrons. Protons and neutrons are not

fundamental particles. They are made up of quarks. A modern view of a fundamental particle is called the

standard model in particle physics. For further information, visit the websites in the Suggested Reading

section of this unit.

Plum-Pudding Model Versus Planetary Model

A widely accepted atomic model in the early 20th century was the Thomson’s plum-pudding model. In 1897,

Thomson discovered the electron, and he became the Nobel Prize laureate in 1906. He thought that the

positive charge is distributed smoothly like pudding and the negatively charged electrons are situated like a

plum. However, his idea was disproved by his student Rutherford’s experiment on alpha particles, which are

the nuclei of helium atoms (Cutnell & Johnson, 2004).

PHS 1110, Principles of Classical Physical Science

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If the plum-pudding model is correct, the ejected alpha particles should go straight through a thin metal foil

because the mass of electrons is relatively small; however, many of the alpha particles were deflected with

significant angles up to 180 degrees. Rutherford was amazed at his experiment. He proposed that the

smoothly distributed positive charge should be concentrated in a small region, the nucleus. In order to explain

how the negatively charged electrons are separated from the positively charged nucleus, he concluded that

the electrons must be moving around the nucleus. If the electrons had no motion, they would be coupled with

the nucleus because of the attractive electric force. He pictured the atomic structure like our solar system, a

planetary model.

Bohr’s Atomic Model for Hydrogen

The motion of the electrons was unstable in the Rutherford model. In order to fix that, Bohr constructed his

atomic model in 1913 (Cutnell & Johnson, 2004). The electrons continuously emit light because they are

accelerating and lose energy on a curved path as they move into the nucleus. Bohr suggested that the

electrons move in fixed orbits and a certain amount of energy can be emitted or absorbed whenever electrons

are jumping down or up into the allowed orbits; this is the quantized shell model. The energy of an electron is

proportional to the size of orbits. When the electron is at the smallest orbit, it is stable; this is the ground state.

Bohr adopted Planck’s quantum idea to explain his atomic model. Planck thought that a basic element of

electromagnetic radiation was a photon. It is true that the Bohr model explains basic mechanics of atomic

structure with a quantum view; however, it fails to reconcile with the uncertainty principle because the Bohr

model is similar to the solar system model. According to the uncertainty principle, we cannot tell the position

and momentum of a particle at the same time (Nave, n.d.). Also, there are no explanations why particular

spectral lines are brighter than others.

Example 1: In the planetary model of the atom, electrons and the nucleus are analogous to the earth and

the sun. Compare the scale of the atomic model to the earth-sun system.

Solution 1: The size of nucleus is about 10-15m. Electrons are located 10-10m from the center of the atom.

That is, the orbital radius of electrons is 100,000 (=10-10 /10-15) times larger than the size of the nucleus. In

our solar system, the orbital radius of the earth is 1.5x1011m and the sun’s radius is about 7x108m. The

ratio between them (1.5×1011/ 7×108) is about 200. The orbital radius of the earth is only about 200 times

larger than the size of the sun. That is, the earth would be located about 500 times greater than the present

position. The earth would be located far beyond the orbit of Pluto. You can say that atoms are mostly empty

space!

PHS 1110, Principles of Classical Physical Science

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The Periodic Table of the Elements

The periodic table of elements

(2012rc, 2009)

The periodic table is a well-organized chart of the elements according to their atomic number (or proton

number), atomic mass, electron configuration, and chemical properties. This table can be found below or in

Figure 11.9 on p. 216 in the textbook.

The mass number is the sum of proton numbers and neutron numbers. More than 100 elements are listed in

the Periodic Table. The most abundant element, an isotope of carbon (C-12), is the reference value to

measure the mass of atoms. The atomic mass of C-12 is 12u (atomic mass unit). 1u=1.66×10-27kg.

Isotopes refer to when the element has the same proton numbers but different neutron numbers in the

nucleus. For instance, isotopes of carbon are C-12, C-13, and C-14. They all have 6 protons, but 6, 7, and 8

neutrons, respectively. The atomic mass in the periodic table is an averaged value of the isotopes of the

element. In the case of carbon, the atomic mass is 12.011, rather than exactly 12u. It reflects the amount of

C-13, which is in about a 1% abundance. The amount of C-14 is negligible.

1. The molecular mass of a molecule is the sum of the atomic masses of its atoms. For instance,

hydrogen and oxygen have atomic masses of 1.0079u and 15.999u respectively (See Figure 11.9 on

p/ 216 in the textbook). Thus, the molecular mass of a water molecule (H2O) is

(2×1.0079u+15.999u=18.0148u). In order to express enormous numbers of atoms or molecules, the

gram-mole, or, more simply, the mole, is used.

2. One gram-mole of a substance contains as many particles (atoms or molecules) as there are atoms

in 12 grams of the isotope carbon-12. According to experiments, 12 grams of C-12 have 6.022×1023

atoms. The number of atoms per mole is called Avogadro’s number.

PHS 1110, Principles of Classical Physical Science

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Hooke’s Law

When a small amount of force applies to matter, the shape of

matter changes a bit. However, it comes back to the original

shape once the applied force is removed; this is elasticity.

Robert Hooke (1635 – 1703) discovered a law of elasticity

(Waggoner, 2001). See Figure 12.7 on p. 231 in the textbook.

The restoring force of an ideal spring is F=-kx, where k is the

spring constant and x is the displacement of the spring from

its original length. The spring constant k [N/m] is often called

the stiffness of the spring. As k is larger, the stiffness of the

spring increases. Remember Newton’s action-reaction law.

The restoring force comes from the applied force, F=kx. The

applied force is proportional to the displacement.

A depiction of Hooke’s Law.

Example 2: An ideal spring is stretched 0.2 meters with k=50 N/m. What is the applied force?

Solution 2: From Hooke’s law, F=kx= 50 x 0.2= 10 N.

Mass Density

The mass density (ρ) is the mass (m) of matter divided by its volume (V), or ρ=m/V. Its unit is kg/m 3. ρ is

proportional to m when V is constant. When m is fixed, ρ is inversely proportional to V.

Example 3: Find the volume occupied by 1 kg of gold.

Solution 3: From Table 12.1 on p. 230 in the textbook, the density of gold is 19300 kg/m 3. Therefore,

V=1/19300 =5.18×10-5 m3.

References

2012rc. (2009). Periodic table large [Online image]. Retrieved from

https://commons.wikimedia.org/wiki/File:Periodic_table_large.svg

Cutnell, J., & Johnson, K. (2004). Physics (6th ed.). Hoboken, NJ: Wiley.

Lawrence Berkeley National Laboratory. (n.d.). Early atomic understanding. Retrieved from

http://www.particleadventure.org/other/history/earlyt.html

Nave, R. (n.d.). Wave nature of electron. Retrieved from http://hyperphysics.phy-astr.gsu.edu/hbase/bohr.html

The atomic model: Atoms, elements, and the periodic table. (n.d.). Retrieved from

https://www.texasgateway.org/sites/default/files/resources/documents/EvolutionOfAtomicModel.pdf

Waggoner, B. (2001). Robert Hooke (1635-1703). Retrieved from

http://www.ucmp.berkeley.edu/history/hooke.html

PHS 1110, Principles of Classical Physical Science

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Suggested Reading

The two resources below were referenced in the unit lesson. The first website is a timeline of particle physics.

Click through the different time periods to read about the theories on particle physics during that time. The

second link explains the standard model in more detail. If you are interested in learning about how the

fundamental building blocks of matter interact, take some time to review this website.

European Organization for Nuclear Research. (n.d.). The standard model. Retrieved from

https://home.cern/about/physics/standard-model

Lawrence Berkeley National Laboratory. (n.d.). Particle physics timeline. Retrieved from

http://www.particleadventure.org/other/history/

Learning Activities (Nongraded)

Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit

them. If you have questions, contact your instructor for further guidance and information.

To practice what you have learned in this unit, complete the following problems and questions from the

textbook. The answers to each problem can be found in the “Odd-numbered Answers” section in the back of

the textbook. The question number from the textbook is indicated in parentheses after each question.

1. What are the five most common elements in humans? (Textbook #17 on p. 223)

2. The average speed of a perfume-vapor molecule at room temperature may be about 300 m/s, but

you’ll find the speed at which the scent travels across the room is much less. Why? (Textbook #39 on

p. 224)

3. The mass numbers of two isotopes of cobalt are 59 and 60. (a) How many protons and how many

neutrons are in each isotope? (b) How many orbiting electrons does an atom of each have when the

atoms are electrically neutral? (Textbook #45 on p. 224)

4. If two protons and two neutrons are removed from the nucleus of an oxygen atom, what nucleus

remains? (Textbook #47 on p. 224)

5. Discuss which contains more atoms: 1kg of lead or 1 kg of aluminum. (Textbook #65 on page 225)

6. If a 1-kg object stretches a spring by 2 cm, how much well the spring be stretched when it supports a

3-kg object? (Assume the spring does not reach its elastic limit.) (Textbook #11 on page 240)

7. If the linear dimensions of an object are doubled, by how much does the surface area increase? By

how much does the volume increase? (Textbook #21 on page 240)

8. A 19.3-g mass of gold in the form of a cube is 1cm long on each side (somewhat smaller than a sugar

cube). What would be the length of the sides of a cube that has twice this mass of gold? (Textbook

#35 on page 241)

9. Consider two bridges that are exact replicas except that every dimension of the larger bridge is

exactly twice that of the other – that is, twice as long, structural elements twice as thick, and so on.

Which bridge is more likely to collapse under its own weight? (Textbook #59 on page 242)

10. Nourishment is obtained from food through the inner surface area of the intestines. Why is it that a

small organism, such as worm, has a simple and relatively straight intestinal track, while a large

organism, such as a human being, has a complex and extensively folded intestinal track? (Textbook

#87 on page 243)

PHS 1110, Principles of Classical Physical Science

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Hints for Unit V Problem-Solving assignment

Dear all,

Please review below before doing your unit 5 assignment.

Questio

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youtube address

1

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2

power

point presentati

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PS V-1.pptx

script

file

PS V1.docx

https://www.youtube.com/watch?v=_TrvLOHXDs&feature=youtu.be

PS V-2.pptx

youtu.be

PS V-3.pptx

PS V-4.pptx

PS V4.docx

PS V-5.pptx

PS V5.docx

PS V-6.pptx

PS V6.docx

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PS V-7.pptx

PS V7.docx

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PS V-8.pptx

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PS V2.docx

PS V3.docx

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PS V8.docx

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PS V-9.pptx

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https://www.youtube.com/watch?v=gxOIdjGgvw&feature=youtu.be

PS V-10.pptx

PS V9.docx

PS V10.doc

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