Introduction to Physical Science

J. M. Veal, Ph. D.

version 18.01.10

Contents

1 Introduction 3

1.1 Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.1 Review of Basic Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.1 Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2.2 Systems & Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Physics 4

2.1 Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.1 Speed, Velocity, & Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.1.2 Circular Motion & Projectiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.1 Newton’s Laws of Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.2 Newton’s Universal Law of Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.3 Buoyancy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2.4 Momentum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.3 Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.1 Work & Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.2 Kinetic & Potential Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.3 Conservation of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.3.4 Exam I . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.4 Heat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.4.1 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.4.2 Phases of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.4.3 Specific & Latent Heats . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.4.4 Heat Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.4.5 Ideal Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.5 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.5.1 Wave Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.5.2 Light & Spectral Bands . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.5.3 Sound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.6 Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.6.1 Reflection & Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.7 Electricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.7.1 Charge & Coulomb’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.7.2 Current, Voltage, & Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.7.3 Transformers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.8 Magnetism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.8.1 Magnetic Dipoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.9 Atoms & Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.9.1 Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.9.2 The Classical Atom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.9.3 Quanta, Absorption, & Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.9.4 Matter Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.9.5 Exam II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.10 Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.10.1 Radioactivity & Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.10.2 Fission & Fusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1

J. M. Veal, Introduction to Physical Science 2

3 Chemistry 93.1 Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1.1 Types of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.2 Periodic Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.3 Electron Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93.1.4 Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.2 Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.1 Two Basic Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.2 Ionic Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103.2.3 Covalent Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.3 Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113.3.1 Acids & Bases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

4 Astronomy 124.1 Solar System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.1.1 Overview of Solar System Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.1.2 Kepler’s Laws of Planetary Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.2 Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2.1 Stellar Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124.2.2 Exam III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2.3 Cosmic Recycling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.2.4 Final Exam . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

4.3 Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134.3.1 Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

A Formulae + Periodic Table 14

Chapter 1

Introduction

1.1 Mathematics

1.1.1 Review of Basic Formulasx

y{z�x � z

y

xyxz � xy�z

x�y �1

xy

x � yz Ñ y � x1{z

1.2 Measurement

1.2.1 Units

• Length, mass, time, & charge (this last to be addressed later)are the four quantities that use standard units alone.

One meter is defined as the distance light in a vacuum travelsin 1/299,792,458 of a second.

One kilogram is defined as the mass of the platinum-irridiumcylinder kept in Paris.

One second is defined as the amount of time it takes a cesiumatom to oscillate 9,192,631,770 times.

• Speed, volume, density, and almost all other quantities usederived units, which are combinations of standard units.Consider examples.

1.2.2 Systems & Conversions

• The modern form of the metric system is the InternationalSystem of Units (a.k.a. SI).

The prefixes deka-, hecto-, kilo-, mega-, & giga- mean 101,102, 103, 106, & 109, respectively.

The prefixes deci-, centi-, milli-, micro-, & nano- mean 10�1,10�2, 10�3, 10�6, & 10�9, respectively.

• Examples of systems are the mks system, the cgs system,and the fss system.1

• Switching from one system to another is known as a conver-sion. Consider converting m.p.h to km/s.

1You should be able to guess what “mks” and “cgs” stand for. The “fss”system refers to “foot-slug-second”.

3

Chapter 2

Physics

• Physics is the most fundamental science: the basic principlesand concepts about how the universe works.

• Of all the scientific disciplines, physics is the least likely tofollow a recipe to solve a problem. Physics problems are abit like riddles. Does your method used to solve one riddleusually help you solve the next riddle?1

2.1 Motion

2.1.1 Speed, Velocity, & Acceleration

• Speed is distance divided by time. For example, 10 m/s is aspeed. Note that v is usually used to represent speed.2 Theaverage speed is vavg � pxf � xiq{ptf � tiq.

• Velocity is speed in a particular direction. For example 10m/s due north is a velocity.

• Acceleration is a change in velocity. For example, 9.8 m/s2

is an acceleration. Note that this can be a change in speedor a change in direction, or both. Average acceleration isaavg � pvf � viq{ptf � tiq.

– If a ball takes time t to fall, from what height h did itstart?

– If a ball falls from height h, how much time t does ittake?

2.1.2 Circular Motion & Projectiles

• Uniform circular motion involves changing direction at con-stant speed; it’s a type of acceleration called centripetalacceleration,3 which is speed squared divided by radius:ac � v2{r. [sketch 1]

• Projectile motion is usually parabolic, which means it fol-lows the shape of an upside-down parabola. (Recall that aparabola has the functional form y 9 x2.) [sketch 2]

The horizontal and vertical components of the motion areindependent of each other!

2.2 Force

• The unit of force is the newton; 1 N = 1 kg�m/s2.

1Consider examples: two buckets, three switches, the color of the bear,buried in the sand, how many latitudes, the Rubik’s cube, and the twelve-coins problem.

2Velocity is more specific than speed, and is usually represented by ~v.3Centripetal acceleration should not be confused with the centrifugal ef-

fect.

2.2.1 Newton’s Laws of Motion

• First. The law of inertia: left undisturbed, a body at restwill remain at rest and a body in motion will remain inmotion in a (straight) line.

Inertia is a body’s resistance to acceleration. Acceleration isa change in speed or direction.

• Second. F � ma: force equals mass times acceleration.4

Mass and weight are not the same. Weight depends on lo-cation; mass doesn’t. Weight is a force.

• Third. Action equals reaction: for every force applied to abody, there exists an equal and opposite force.

Consider a collision between billiard balls. [sketch 3]

2.2.2 Newton’s Universal Law of Gravitation

• F � GMm{d2

Here, F is the gravitational force between two masses, G isthe gravitational constant (a.k.a. Newton’s constant), M &m are the masses, and d is the distance between the centersof the two masses. This is an “inverse-square law”; considerexamples,5 including weight.

2.2.3 Buoyancy

• The density of an object is the mass divided by the volume:ρ � m{V .

• An object in a fluid will sink if ρo ¡ ρf . It will have neutralbuoyancy if ρo � ρf . It will rise to the surface and float ifρo   ρf .

2.2.4 Momentum

• Linear momentum is mass times speed: p � mv. Note that,in this case, big & slow can be the same as small & fast.

• Angular momentum is mass times speed times radius: ` �mvr.

• Conservation of momentum, linear or angular, is one of thefundamental laws of the universe. When a quantity is con-served, its final value is the same as its initial value: pf � pi,and `f � `i. These equations can also be written using theupper-case greek letter delta: ∆. That is, ∆p � pf � pi. Sowe have ∆p � 0, and ∆` � 0.

4Actually ~F � d~p{dt.5WSS 180 6-1 (15’), WU 100 3-1, 3-2 (25’)

4

J. M. Veal, Introduction to Physical Science 5

The linear case is readily observed in the behavior of billiardballs. The angular case can be thought of as the “spinningice-skater effect”. [sketch 4] Consider examples.

2.3 Energy

• The unit of energy is the joule; 1 J = 1 N�m.

2.3.1 Work & Power

• Work is related to force times distance: W � Fd. Here, Fis the part of the force parallel to the distance.

• Power is energy divided by time: P � E{t.

2.3.2 Kinetic & Potential Energies

• Kinetic energy, or energy of motion, is half of the mass timesthe square of the speed: K � mv2{2.

• Gravitational potential energy, often associated with the en-ergy of an object before it falls, is the mass times the acceler-ation due to gravity times the height: U � mgh. Note thatthe location at which h � 0 may be chosen for convenience.

• The total energy6 is the sum of the kinetic plus potentialenergies: E � K � U .

2.3.3 Conservation of Energy

• Total energy is conserved: ∆E � 0.

Consider the example of a swinging pendulum. [sketch 5]Here we see that ∆E � 0 is a very useful equation, able tomake complicated problems relatively simple.

2.3.4 Exam I

Exam 1 covers material up to here.

2.4 Heat

• Heat is energy in transit. One common unit of heat is thecalorie: 1 cal = 4.2 J, 1 Cal = 1 kcal. One calorie is theamount of energy needed to increase the temperature of onegram of water by one kelvin.7

2.4.1 Temperature

• What is it? What is the physical difference between hotwater and cold water? Temperature is the measurement ofthe speed of the particles (e.g., atoms, molecules).

• Consider scales and units. � F, � C, K.

scale freeze boil� F 32 212� C 0 100K 273 373

6More specifically, we mean the total mechanical energy.7This is not true in the case of latent heat.

How cold can something get? In accordance with our defi-nition, it’s when the motion of atoms is as slow as possible.This is “absolute zero”; this is 0 Kelvins.

2.4.2 Phases of Matter

• There are three phases of matter: solid, liquid, & gas. Themicroscopic structure of a solid is called a lattice, which hasa set volume and a set shape. A liquid is a fluid with a setvolume but no set shape. A gas is a fluid with no set volumeand no set shape.

2.4.3 Specific & Latent Heats

• Specific heat is related to the heat required to increase thetemperature of an object. H � mc∆T . Given a mass m, His the amount heat reqired to increase the temperature by∆T . The specific heat is c; it has units of J/kg�K.

• Latent heat is the heat used to produce a phase transitionsuch as melting (solid becomes liquid) or boiling (liquid be-comes gas.)8 Latent heat is released during a phase transi-tion such as condensing (gas to liquid) or freezing (liquid tosolid). [sketch 6]

2.4.4 Heat Transfer

• There are three modes of heat transfer.

Conduction is the result of molecular collisions and vibra-tions. (What is a burn?)

Convection involves moving cells of fluid. This is similar toboiling water. [sketch 7]

Radiation is electromagnetic energy, like sunlight.

2.4.5 Ideal Gases

• An ideal gas is one that obeys the following relationship be-tween pressure, volume, and temperature. pV9NT . Here,N is the number of particles (atoms or molecules) of gas. IfN doesn’t change, then pV {T is constant.

2.5 Waves

2.5.1 Wave Properties

• Consider a sine wave as opposed to a breaking wave. [sketch8] Wavelength is the distance from one crest to the next.Amplitude is the height of the wave; this is related to thewave’s power. Frequency is the number of crests passing byeach second. [sketch 9] Generally, v � wf .

• Spherical waves diminish as the inverse square of the dis-tance. [sketch 10]

2.5.2 Light & Spectral Bands

• White light (for example, sunlight) is actually a sum of col-ors. The speed of light is c � 300, 000 km/s. This is likegoing around the ` 7 times in one second.

• Light is a wave. Generally, c � wf .

8In the case of dry ice or a comet, the matter can skip the liquid phase.This is known as sublimation (solid becomes gas).

J. M. Veal, Introduction to Physical Science 6

• What is the physical difference between red light and bluelight? Consider spectral bands: radio, microwave, infrared,visible, ultraviolet, x-ray, and γ-ray. [sketch 11]

• Consider the electric and magnetic waves. [sketch 12]

2.5.3 Sound

• A sound wave is a longitudinal wave, having compressionsand rarefactions (as opposed to a transverse wave whichhas “crests” and “troughs”). [sketch 13] (Why can we hearsomeone clap?)

• The intensity of sound is the power per area. The unit isthe decibel9 (dB), which is (1/120) W/m2.

If I � 2I0 in W/m2, then I � I0 � 3 in dB. If I � 10I0 inW/m2, then I � I0 � 10 in dB.

• It’s possible to shatter a goblet with a sound wave using aphenomenon known as resonance.10

It’s similar to pushing someone on a swing. [sketch 14] Eachsuccessive applied force may be very weak, but each is ap-plied at exactly the right time, the results can be dramatic.[sketch 15]

2.6 Optics

2.6.1 Reflection & Refraction

• The law of reflection simply says the angle of incidenceequals the angle of reflection: θi � θr.

• Refraction is the bending of light as it goes from one mediumto another. The index of refraction of a medium is ratioof the speeds of light in a vacuum to that in the medium:n � c{v.

2.7 Electricity

2.7.1 Charge & Coulomb’s Law

• Electric charge is one of the four fundamental quantities (likelength, mass, and time) that has a standard unit. In thiscase, it’s the coulomb. The charge on an electron is about�1.6� 10�19 C.

• Coulomb’s law is to charge as Newton’s law of gravitation isto mass. Fe � kq1q2{d

2. Charge can be positive or negative,and so can the electric force. A positive force is repulsive;a negative force is attractive. This is why opposite chargesattract and like charges repel.

2.7.2 Current, Voltage, & Power

• Electric current is charge divided by time: i � q{t. The unitof current is the ampere (or amp for short): 1 A = 1 C/s.It describes how much charge is passing by in one second.

9This is one tenth of a bell.10Check out YouTube: “breaking a wine glass using resonance” (done at

USC). Note that the collapse of the Tacoma-Narrows Bridge in 1948 was notdue to resonance; it was due to aeroelastic flutter.

• Electric voltage is the work per charge: V � W {q. It isalso the current times the resistance: V � iR. The unit ofvoltage is the volt: 1 V = 1 J/C.

• Electric power is the current times the voltage: P � iV . It isalso the square of the current times the resistance: P � i2R.As before, the unit of power is the watt.

2.7.3 Transformers

• A transformer is a device that converts one voltage to an-other according to the “number of turns” in each inductor,a.k.a. solenoid : V2 � pN2{N1qV1.

2.8 Magnetism

2.8.1 Magnetic Dipoles

• What happens if we break a magnet in half? What aboutmagnetic splinters, atoms, and subatomic particles? [sketch16]

• Magnetic dipoles have a force between them: F �kmp1p2{d

2. Note that the dipole strength, p, can be pos-itive or negative. This allows Fm to be positive or negative.

The Earth has a dipolar magnetic field, with an axis tiltedrelative to the rotation axis by about 13�.11 [sketch 17]

2.9 Atoms & Light

2.9.1 Photons

• The Duality of Light: Light is a particle and a wave andneither.

A particle of light is called a photon.

When an experiment is performed that will work only if lightis a wave and that will fail if light is a particle, it works. Butwhen an experiment is performed that will work only if lightis a particle and that will fail if light is a wave, it works.The only possible conclusion is that light is a particle and awave and neither!

• This is not intuitive – we don’t grow up with this kind ofthing as part of our daily reality. So we find that the universeis a strange, exotic, wonderful place. And we learn thatthings can exist even if they don’t fit our common sense andintuition.12

2.9.2 The Classical Atom

• “Classical” implies an older, less accurate, but simpler idea.Consider a simple atom: nucleus and electron. [sketch 18]

• The atomic number tells us the element and equals the # ofprotons in the nucleus.

The atomic weight tells us the isotope and equals the # ofnucleons in the nucleus. (A nucleon is a proton or a neutron.)

The atomic charge tells us the ion and equals the # of pro-tons in the nucleus minus the # of electrons in the atom.

11Strictly speaking, the relative tilt is 77� � π � 13�, and the south mag-netic pole is the geomagnetic north pole.

12All these years this amazing object, light, has been all around you; didyou ever stop to consider its true nature?

J. M. Veal, Introduction to Physical Science 7

• Consider examples. How many protons, neutrons, and elec-trons are in each? 1H, 2H, 4He, 3He�, 3He��, 8Li, 60Fe���

p�: a.n.

n: a.w. - a.n.

e�: a.n. - a.c.

2.9.3 Quanta, Absorption, & Emission

• Consider the ground state and an excited state. Ground statemeans the e� has the minimum possible energy, and excitedstate means e� has more than the minimum possible energy.There are many levels (a.k.a. states, orbitals) available to ane� in an atom. A higher level for an e� means it has moreenergy. [sketch 19]

Only certain levels are allowed for the e�; anything in be-tween is forbidden. [sketch 20] This is the Bohr model ofthe atom.

The atom can only have specific quantities of E. We say “en-ergy is quantized”. What does this imply? This is differentfrom the way things work in our everyday world. Imag-ine a car accelerating from 50 mph to 60 mph. Can thecar go from 50 to 60 without at some point having everyspeed in between? But jumping this way is exactly whatelectrons do. If cars behaved like electrons, they could in-stantaneously leap from 50 mph to 60 mph. When electronsjump from one level to the next, they never have the energyin between; they never even occupy the space in betweenthe levels. They make a “quantum leap”. [previous sketch](Imagine if you have no money and I then give you a $50bill. Did you at any time have $20?)

• What makes an electron jump up from one level to the next?The atom absorbs energy. What kind of energy? Light (pho-tons). When an atom absorbs a photon, the e� jumps up toa higher level; this is absorption. [sketch 21]

E � hf : E is energy of the photon, f is frequency, and his a constant (a number, sort of like G in gravity, but evensmaller). So we see a blue photon has more E than a redphoton

Since only specific levels are allowed, only specific colors canbe absorbed by an atom. That is, the photon has to havejust the right E (which determines w and f) in order to beabsorbed and make the e� jump from one level to exactlyanother; if the photon has too much or too little, then itwill pass right through the atom. There must be a perfectmatch.

Absorption is basically photon in, e� up.

• Electrons, when left alone, seek the ground state. This isbecause the ground state has the lowest energy. This ismuch like how a ball, left alone on a hill, will roll to thelowest point. This is because the lowest point has the lowestenergy.

Emission of a photon occurs when an electron jumps to alower level. This is the opposite of absorption. [sketch 22]

Since only specific levels are allowed, only specific colors canbe emitted by an atom.

Emission is basically e� down, photon out.

• Consider the example of phosphorescence, which is delayedemission (glow-in-the-dark), involving a metastable state.[sketch 23]

2.9.4 Matter Waves

• As all waves can be interpreted as particles, so can all par-ticles be interpreted as waves, with a de Broglie wavelengthequal to Planck’s constant divided by momentum: w � h{p.(Recall p � mv.)

2.9.5 Exam II

Exam 2 covers material between exam 1 and here.

2.10 Nuclei

2.10.1 Radioactivity & Reactions

• Radioactivity is the spontaneous decay (a.k.a. spontaneousdisintegration) of an atomic nucleus. Any one (or more) ofthe following three basic criteria will cause a nucleus to beradioactive: more than 83 protons, more protons than neu-trons (except 1H and 3He), or odd numbers of both protonsand neutrons (except 2H, 6Li, 10B, and 14N).

– An example of alpha decay is 238U Ñ 234Th + 4He,which is named for the α-particle: a 4He nucleus.

– An example of beta decay is 14C Ñ 14N + e�, which isnamed for the β-particle: an e�.

• The half-life of a radioactive element is the amount of timeit takes for half of the atoms in a sample of the element todecay.

The function can be graphed: f � p1{2qn. [sketch 24] Here,f is the fraction left of the original sample and n is thenumber of half-lives that have passed.

We can estimate the age of the sample: a � nt. Here, a isthe age and t is the half-life.

– Let f � p1{2qn be solved for n: n � rln f s{rln p1{2qs.Then we find the age is a � rln f s{rln p1{2qst.

What if t � 10, 000 years and f � 1{8?

• The principle underlying all nuclear reactions is the inter-changability of mass and energy: E � mc2. The totalamount of “mass-energy” in the universe is thought to beconstant; it can be neither created nor destroyed.

• There are a few rules that go along with nuclear fusion reac-tions. Here we are concerned with two of them: conservationof charge and conservation of nucleons (a proton or a neu-tron is a nucleon). In physics, when something is conserved,the total amount doesn’t change.

J. M. Veal, Introduction to Physical Science 8

2.10.2 Fission & Fusion

• Nuclear fission is the splitting of an atomic nucleus. For ex-ample, an unstable uranium atom may be split into kryptonand barium: 235U + n Ñ 142Ba + 92Kr + 2n + energy. Thisparticular fission reaction is an example of neutron scatter-ing, and was once used to make nuclear weapons known asneutron bombs (a.k.a. fission bombs). We note the impor-tant distinction between subcritical and supercritical masses.[sketches 25 & 26]

Fission is used in nuclear power plants: San Onofre andelsewhere around the world.

• Nuclear fusion is the joining of two atomic nuclei. The mostcommon nuclear fusion reaction is happening in our Sun andin most stars: the proton-proton chain reaction, which con-verts H to He plus energy.13 This fusion reaction is used tomake nuclear weapons known as hydrogen bombs (a.k.a. fu-sion bombs).

Fusion is studied in a type of experiment called a tokamak.There is a tokamak in San Diego.

• Briefly consider the chart of nuclides.

13The reaction is much more interesting than just 41H Ñ 4He + energy.[sketch 27]

Chapter 3

Chemistry

• Chemistry is the science of the composition & structure ofmatter and the reactions that change substances into othersubstances.

3.1 Elements

3.1.1 Types of Matter

• An element has all atoms the same.

• A compound has all molecules the same, with at least twoelements per molecule.

• There are two types of mixtures. Examples of a homogeneousmixture (a.k.a. solution) are air, saltwater, and bronze (Cu,Sn). Examples of a heterogeneous mixture are spaghetti withmeatballs and chocolate chip ice cream.

• There are two special cases of molecules. The diatomicmolecules are H2, N2, O2, F2, Cl2, Br2, & I2. An exam-ple of an allotrope is carbon, because pure carbon can bediamond or graphite.1

3.1.2 Periodic Table

• In 1869, D. Mendeleev2 put the elements into a table;3 therewere 63 known by that time.

• Properties of different elements follow trends. These proper-ties are periodic, or repeating, functions of atomic number.

Horizontal rows are periods; columns are groups.

• Metallic character increases downward and to the left.(Some are “semimetals”.)

Consider standard temperature and pressure. There are twoliquids: Br & Hg. There are five diatomic gases: H, N, O,F, & Cl. There are six noble gases: He, Ne, Ar, Kr, Xe, &Rn. The rest are solid.

3.1.3 Electron Configurations

• The principle quantum number, represented by n, tells usthe energy level, or shell, of an electron in an atom.

The outer shell is the valence shell. The electrons in thevalence shell, known as valence electrons, are the ones thatform chemical bonds.

1There are many allotropes of carbon.2Pronounced “men-duh-LAY-eff”.3See ptable.com.

• An element’s placement in the periodic table indicates somedetail about the electron configuration. The period numberequals the number of shells in the atom. The group numberequals the number of valence electrons. This last is true forrepresentative elements only. These are the first two groupson the left and the last six groups on the right. The elementsinbetween are the transition metals. [sketch 28]

• The size of an atom increases downward in the table becausethe farther down the table, the more shells the atom has.The size of an atom increases to the left in the table becausethe farther to the left, the fewer unshielded protons are feltby each electron in the valence shell. [sketch 29]

3.1.4 Nomenclature

• A known compound has a chemical formula, for example,H2O.

• Some compounds have special names. A few of theseare as follows, some of which are aqueous solutions (aq).

formula compoundH2O waterNH3 ammoniaCH4 methaneN2O nitrous oxideNO nitric oxideHCl hydrochloric acid

,//////.//////-

aq

HNO3 nitric acidCH3CO2H acetic acidH2SO4 sulfuric acidH2CO3 carbonic acidH3PO4 phosphoric acid

• Metal plus nonmetal. For a binary compound, list the metalfirst and then the nonmetal with an -ide suffix. For example,KF is potassium fluoride. This rule holds as long as themetal forms only one ion, such as Group 1A, Group 2A, andAl, Zn, & Ag.4

• Two nonmetals. List the more metallic element and then theless metallic element with an -ide suffix. Use Greek prefixesto designate multiple atoms: mono- (rarely used), di-, tri-, tetra-, penta-, hexa-, hepta-, & octa- (either on the firstelement, or the second element, or both). For example, COis carbon monoxide.

• Polyatomic ions. Some have special names. (Note -ate vs-ium.)

4What is an ion? What charges do these ions have? Why?

9

J. M. Veal, Introduction to Physical Science 10

formula compoundC2H3O�

2 acetateHCO�

3 bicarbonateOH� hydroxideNO�

3 nitrateCO2�

3 carbonateSO2�

4 sulfatePO3�

4 phosphateNH�

4 ammonium

• Metal plus polyatomic ion. List the metal and then the poly-atomic ion. For example, NaNO3 is sodium nitrate.

• Hydrogen plus polyatomic ion. This is called an acid. (Seetable above.)

• Ammonium plus nonmetal. List ammonium and then thenonmetal with an -ide suffix. For example, NH4Cl is ammo-nium chloride.

• Ammonium plus negative polyatomic ion. List ammoniumand then the ion. For example, (NH4)2SO4 is ammoniumsulfate.

3.2 Bonds

3.2.1 Two Basic Laws

• The law of mass conservation declares that no detectablechange in total mass occurs during a chemical reaction(A. Lavoisier5)

If (a kg of X) + (b kg of Y) Ñ (c kg of Z), then a � b � c.For example, (16 kg of O) + (2 kg of H) Ñ (18 kg of H2O).

• The law of definite proportions declares that the relativeproportions of elements in a compound are constant; thatis, it does not depend on the sample size.

If there are u kg of compound Z, which is made of elementsX & Y, and X/Y� r, then X/Y� r is also true for v kg ofcompound Z. For example, 28 kg of CO has 12 kg of C and16 kg of O, so r � 12{16 � 3{4. Therefore 56 kg of CO musthave 24 kg of C and 32 kg of O, since 24{32 � 3{4 � r (thesame r).

• As an example, consider Al2O3.

– The percent by number of atoms is 40% Al and 60% O,because 2/(2+3) = .4 and 3/(2+3) = .6.

– The percent by mass can be readily found as well.There is a general formula to be used with any com-pound: PX � 100 � nX � amuX{fm. Here, PX is thepercent of the compound made of element X, nX is thenumber of atoms of element X in the chemical formula,amuX is the number of atomic mass units in one atom6

of element X, and fm is the formula mass of the com-pound.

∗ So let X be Al. Then nAl � 2, amuAl � 27, andfm � 27 � 2 � 16 � 3 � 54 � 48 � 102. So PAl �100 � 2 � 27{102 � 52.9%.

5Pronounced “lah-vwa-ZHAY”.6This is essentially the atomic weight of the element in the periodic table.

∗ So let X be O. There are two ways to answer, so wecan check our work. The first way is the easiest;100 � 52.9 � 47.1, so PO � 47.1%. The secondway is to use the general formula. Now nO � 3,amuO � 16, and fm � 102 (the same). So PO �100 � 3 � 16{102 � 47.1%.

3.2.2 Ionic Bonds

• The octet rule. When an atom joins other atoms to forma compound, it will either gain, lose, or share its valenceelectrons. It will do this in a way that tends to result inhaving eight electrons in its outer shell. Atoms join untilthe compound is neutral. The exception is H, which tendstoward two (doublet) instead of eight (octet).

For example, consider NaCl. Before Na and Cl join, howmany valence electrons does each have? So Na gives one toCl, and then they’re Na� and Cl� (ions). Now how many va-lence electrons does each have? Recall that opposite chargesattract. So they bond to each other and we have an ioniccompound, and it’s neutral.

And consider MgS. Before? Mg2� & S2�? After? Yet an-other ionic compound, and it’s neutral.

Likewise, consider MgCl2; it’s neutral.

What about Ne, Ar, Kr, Xe, & Rn? They are “noble gases”;they don’t interact. They are chemically inert.

• Consider the lattice of NaCl. It’s a crystal, which means theexternal symmetry results from the molecular structure ofthe lattice. The macroscopic structure is an excellent clueabout the microscopic structure (or nanoscopic).

Is it possible to define one molecule of the lattice? No.[sketch 30]

• Positive ions are cations; negative ions are anions. Whywould metals become cations while nonmetals become an-ions?

• What about C or Si? They would have to gain or lose fourelectrons, which is too difficult. So not all bonds are ionic.

3.2.3 Covalent Bonds

• In a covalent bond, electrons are not gained or lost, they areshared in pairs.

Consider H2 before, during, and after bonding. [sketches31, 32, & 33] Electrons repel each other, protons repel eachother, each proton attracts each electron, and each electronattracts each proton. There is a balance of forces at d=0.074nm. [sketch 34]

• Consider water. Before bonding, how many valence electronsin O? H? H? (6, 1, 1) The O shares one with H, and the Hshares one with O. The same is true for the second H atom.Now how many valence electrons? (8, 2, 2) The octet rule issatisfied.

Consider NH3.

Consider CH4.

J. M. Veal, Introduction to Physical Science 11

3.3 Reactions

3.3.1 Acids & Bases

• Aqueous acids and bases result from ions. For acid, the ionis either H� (hydrogen ion) or H3O� (hydronium ion). Forbase, the ion is OH� (hydroxide ion).

• HCl + H2O Ñ H3O� + Cl� (strong)

CH3CO2H + H2O ��������� H3O� + CH3CO�2 (weak)

NH3 + H2O ��������� NH�4 + OH� (weak)

H2O + H2O ������������������ H3O� + OH� (very weak, neutral)

Note that in all but the first of these four reactions the re-verse reaction dominates – very much so in the last.

• If a solution has more H3O� than OH�, then it’s an acid.If a solution has more OH� than H3O�, then it’s a base.

• The pH scale quantifies the acidity of the solution. Theterm pH stands for “power of hydrogen”. If pH = 7, thenthe solution is neutral. If -1 ¤ pH ¤ 6, then it’s acidic. If 8¤ pH ¤ 15, then it’s basic.

The pH scale is logarithmic. For example, pH = 2 is tentimes more acidic than pH = 3. And pH = 12 is ten timesmore basic than pH = 11.

• Consider the pH of various substances. [sketch 35]

Chapter 4

Astronomy

• Astronomy is the branch of physics concerned with every-thing beyond the Earth.

4.1 Solar System

4.1.1 Overview of Solar System Objects

• Our discussion of planets1 will be relatively brief. Pleaserefer to the textbook for more details.

• Remember the order of the planets with a mnemonic devicelike “My very educated mother just served us nachos.”

• Planets are often studied in groups. Since the planets withina group often have several characteristices in common, ourunderstanding of one planet can be enhanced by researchinganother. This approach is known as comparative planetology.

• The first group is the terrestrial planets and our Moon: Mer-cury, Venus, Earth, Mars, & Moon.

• The second group of planets is the jovian planets (a.k.a. gi-ant planets, gas giants): Jupiter, Saturn, Uranus, & Nep-tune.

• Other classes of solar system objects include dwarf planets2

(Ceres, Pluto, Haumea, MakeMake, Eris, and maybe Sedna),moons in general (Earth has one, Mars has two, Jupiter hasmore than 60, Saturn has more than 60, Uranus has at least25, and Neptune has at least 13), rings, asteroids, comets,and TNO’s (that is, trans-Neptunian objects, which includethe Kuiper belt, the scattered disk, and the Oort cloud).

4.1.2 Kepler’s Laws of Planetary Motion

• First. The law of ellipses: a planet orbits the d in an ellipsewith the d at one focus. [sketch 36]

What exactly is an ellipse? (Consider 2 nails & string.)[sketch 37]

• Second. The law of equal areas: a “planet-Sun line” sweepsout equal areas in equal times. [sketch 38]

1WSS 100 2-1 (8’)2A dwarf planet must meet three criteria. First, it must orbit a star, as

opposed to a planet or a dwarf planet. Second, it must be massive enoughto be spherical, so that it may overcome compressive strength and achievehydrostatic equilibrium. Third, it must not be massive enough to clear itsorbit of planetessimals – by collision, capture, gravitational disturbance, orestablishment of orbital resonances that prevent collisions.

• Third. The harmonic law: P 2 � a3

Here, P is the orbital period and a is the semi-major axis,which is half of the major axis of the ellipse.3 The unit of Pmust be the year and the unit of a must be the astronomicalunit (a.k.a. AU), which is the average distance between theSun and the Earth. Consider Jupiter (5.2, 11.8) or Saturn(9.5, 29.5).

Kepler was the first to be able to create a scale model of thesolar system. [sketch 39]

4.2 Stars

4.2.1 Stellar Evolution

• Stellar evolution is the branch of astronomy that studies howstars change over time.

• A star with H fusion in the core will be in hydrostatic equi-librium; usually a star is in balance with itself. The inwardforce of gravity is balanced by the outward force related tothe energy of nuclear fusion. [sketch 40] As a result, ourSun’s size stays relatively constant.

• Hydrostatic equilibrium lasts for about 1010 years for ourSun with core H fusion. A very massive star,4 about 120Md,will fuse H in the core for about 3�106 years, while the leastmassive star, about .08 Md, will fuse H in the core for about1012 years.5

• As the nuclear fuel burns in the core of a star, heavier ele-ments are built. Late in our Sun’s life, the He in the corewill fuse into C and O. Late in the life of a “supergiant”,many of the elements up to and including Fe will be built inthe stellar core.

A star like our Sun ends up ejecting its outer layers as aplanetary nebula, in which much of the material is deliveredback to interstellar space. The core left behind is a whitedwarf.

A very massive star, like a supergiant, ends up destroyingitself as a supernova, in which elements heavier than Fe arebuilt. The supernova explosion then delivers most of theelements on the periodic table back to interstellar space.The core left behind might be a neutron star or a black hole.

3Newton found Kepler’s third is actually pP {2πq2 � a3{rGpM �mqs.4The “Eddington limit” means if there is too much mass, the fusion will

be too great for the gravity; hydrostatic equilibrium will not be attained andthe star won’t be able to form. This limit is around 300 Md.

5The lifetime on the main sequence can be estimated with t �1010yrs{M2.5.

12

J. M. Veal, Introduction to Physical Science 13

4.2.2 Exam III

Exam 3 covers material between exam 2 and here.

4.2.3 Cosmic Recycling

• Where did the carbon and oxygen atoms in our bodies comefrom? Our iron atoms and our heavier elements?

The star-gas-star cycle is self-explanatory. Stars endtheir lives as planetary nebulae or supernovae, sendingtheir “newly constructed” elements back to the interstellarmedium. Some of the ISM becomes interstellar dust. Subse-quently, this interstellar dust and gas collapses to form newstars. The cycle continues. We are recylcled star material.6

• What if some of our protons could tell their stories? Eachwould have its own unique 13.8 billion-year story to tell.If we could speak with one of our protons, we could ask itquestions. Where were you ten billion years ago? Six billion?Of how many stars have you been a part? Where were youone billion years ago? Ten thousand? One hundred? Oneyear ago? Where do you see yourself in ten billion years?

Each of us is an astounding collection of nearly 1028 protons– many of the protons having journeys as old as the uni-verse – that have come together after billions of years. Howamazing!

• When I look into the sky I know the stars built you and me,and one day you and I will build them in return.

4.2.4 Final Exam

The final exam is cumulative up to this point.

4.3 Universe

4.3.1 Cosmology

• Discussion.

6WU 180 2-1 (11’)

Appendix A

Formulae + Periodic Table

vavg �xf � xitf � ti

aavg �vf � vitf � ti

h �1

2gt2

ac �v2

r

F � ma

F �GMm

d2

ρ �m

Vp � mv

` � mvr

∆p � 0

∆` � 0

W � Fd

P �E

t

K �1

2mv2

U � mgh

E � K � U

∆E � 0

H � mc∆T

pV9NT

v � wf

c � wf

θi � θr

n �c

v

Fe �kq1q2d2

i �q

t

V �W

q

V � iR

P � iV

P � i2R

V2 �

�N2

N1

V1

Fm �kmp1p2d2

E � hf

rn � 0.053n2 nm pn � 1, 2, 3, . . .q

En ��13.60

n2eV pn � 1, 2, 3, . . .q

f �

�1

2

n

a � nt

PX �100 � nX � amuX

fm

P 2 � a3

14

J. M. Veal, Introduction to Physical Science 15

Per

iodi

c Ta

ble

of th

e E

lem

ents

C

hem

istr

y R

efer

ence

She

et

Cal

iforn

ia S

tand

ards

Tes

t

Sod

ium

22

.99

Na

11

Ele

men

t sym

bol

* E

lem

ent n

ame

Hyd

roge

n 1.

01

H

1

Lith

ium

6.

94

Li 3

Sod

ium

22

.99

Na

11

39.1

0

19

K

58.6

9

Ni

28

Rub

idiu

m

85.4

7

Rb

37

140.

91

Pr

59

(261

)

Rf

104

95.9

4

Mo

42

(258

)

Md

10

1

72.6

1

Ge

32

1 1A

2

2A

1 2 3 4

7

7B

11

1B

12

2B

13

3A

16

6A

8

5 6 7

9

8B

10

14

4A

15

5A

17

7A

18

8A

3

3B 4

4B

5

5B

6 6B

Cop

per

63.5

5

Cu

29

Cob

alt

58.9

3

Co

27

Hel

ium

4.

00�

He 2

Bor

on

10.8

1

B

5

Car

bon

12.0

1�

C

6

Nitr

ogen

14

.01

N

7

Oxy

gen

16.0

0

O

8

19.0

0�

F

9

Neo

n 20

.18�

Ne

10

26.9

8

Al

13

Sili

con

28.0

9�

Si

14

30.9

7

P

15

Sul

fur

32.0

7

S

16

35.4

5

Cl

17

Arg

on

39.9

5

Ar

18

Cal

cium

40

.08

Ca

20

Sca

ndiu

m

44.9

6

Sc

21

Tita

nium

47

.87

Ti

22

Chr

omiu

m

52.0

0

Cr

24

Iron

55

.85

Fe

26

Zin

c 65

.39

Zn

30

Gal

lium

69

.72

Ga

31

Ars

enic

74

.92

As

33

Sel

eniu

m

78.9

6

Se

34

Bro

min

e 79

.90

Br

35

83.8

0

Kr

36

Str

ontiu

m

87.6

2

Sr

38

88.9

1

Y

39

Zirc

oniu

m

91.2

2

Zr

40

Nio

bium

92

.91

Nb

41

(98)

Tc

43

Rut

heni

um

101.

07

Ru

44

Rho

dium

10

2.91

Rh

45

106.

42

46

107.

87

Ag

47

Cad

miu

m

112.

41

Cd

48

Indi

um

114.

82

In

49

Tin

11

8.71

Sn

50

121.

76

Sb

51

127.

60

52

Iodi

ne

126.

90

I 53

Xen

on

131.

29

Xe

54

Ces

ium

13

2.91

Cs

55

137.

33

Ba

56

138.

91

La

57

Haf

nium

17

8.49

Hf

72

180.

95

73

183.

84

W

74

Rhe

nium

18

6.21

Re

75

Osm

ium

19

0.23

Os

76

192.

22

Ir

77

195.

08

Pt

78

Gol

d 19

7

79

200.

59

Hg

80

Tha

llium

20

4.38

Tl

81

Lead

20

7.2

Pb

82

208.

98

Bi

83

(209

)

84

Ast

atin

e (2

10)

At

85

Pd

Rad

on

(222

)

Rn

86

(223

)

Fr

87

Rad

ium

(2

26)

Ra

88

Act

iniu

m

(227

)

Ac

89

Dub

nium

(2

62)

Db

10

5

Sea

borg

ium

(2

66)

Sg

10

6

(264

)

Bh

10

7

Has

sium

(2

69)

Hs

108

(268

)

Mt

109

140.

12

Ce

58

Neo

dym

ium

14

4.24

Nd

60

Pro

met

hium

(1

45)

Pm

61

150.

36

Sm

62

Eur

opiu

m

151.

96

Eu

63

Gad

olin

ium

15

7.25

Gd

64

158.

93

Tb

65

Dys

pros

ium

16

2.50

Dy

66

Hol

miu

m

164.

93

Ho

67

Erb

ium

16

7.26

Er

68

Thu

lium

16

8.93

Tm

69

Ytte

rbiu

m

173.

04

Yb

70

Lute

tium

17

4.97

Lu

71

232.

04

Th

90

Pro

tact

iniu

m

231.

04

91

238.

03

U

92

Nep

tuni

um

(237

)

Np

93

Plu

toni

um

(244

)

Pu

94

(243

)

Am

95

(247

)

Cm

96

(247

)

Bk

97

(251

)

Cf

98

Ein

stei

nium

(2

52)

Es

99

(257

)

Fm

10

0

Nob

eliu

m

(259

)

No

10

2

(262

)

Lr

103

Mag

nesi

um

24.3

1

Mg

12

9.

01

Be 4

50.9

4

V

23

Man

gane

se

54.9

4

Mn

25

*

Ato

mic

num

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Ave

rage

ato

mic

mas

s

Pot

assi

um

Nic

kel

Pra

seod

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m

Rut

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m

Mol

ybde

num

Men

dele

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Ger

man

ium

Key

Flu

orin

e

Alu

min

um

Pho

spho

rus

Chl

orin

e

Kry

pton

Yttr

ium

Te

chne

tium

P

alla

dium

S

ilver

A

ntim

ony

Tellu

rium

Te

Bar

ium

La

ntha

num

Ta

ntal

um

Ta

Tung

sten

Ir

idiu

m

Pla

tinum

6.

9

Au

M

ercu

ry

Bis

mut

h P

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ium

P

o

Fran

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B

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m

Mei

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ium

Cer

ium

S

amar

ium

Te

rbiu

m

Tho

rium

P

a U

rani

um

Am

eric

ium

C

uriu

m

Ber

keliu

m

Cal

iforn

ium

F

erm

ium

La

wre

nciu

m

Ber

ylliu

m

Van

adiu

m

If th

is n

umbe

r is

in p

aren

thes

es, t

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i

t ref

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to th

e at

omic

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s of

the

m

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tabl

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e.

Co

pyr

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t ©

200

3 C

alifo

rnia

Dep

artm

ent

of

Ed

uca

tio

n