1

The Scientific Method

1. Observe some aspect of the universe.

2. Invent a tentative description, called a hypothesis, that is consistent with what you have observed.

3. Use the hypothesis to make predictions.

4. Test those predictions by experiments or further observations and modify the hypothesis in the light of your results.

5. Repeat steps 3 and 4 until there are no discrepancies between theory and experiment and/or

observation.

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Science versus Pseudoscience

The scientific method is unprejudiced. A theory is accepted based only the results obtained

through observations and/or experiments which anyone can reproduce.

The results obtained using the scientific method are repeatable.

a theory must be ``falsifiable''. Pseudoscience, in contrast, does not employ the

scientific method and is constructed in such a fashion that its claims are not falsifiable

3

System of Units Scientific International (SI)

Based on multiples of 10 meter (m) distance length of the path travelled by light in

vacuum during a time interval of 1/299 792 458 of a second.

kilogram (kg) mass mass of the international prototype of the kilogram.

second (s) time the duration of 9 192 631 770 periods of the radiation

corresponding to the transition between the two hyperfine levels of the ground state of Cs 133

ampere (A) electric current current, if maintained in two straight parallel conductors of

infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 × 10-7 newton per meter of length."

kelvin (K) temperature the fraction 1/273.16 of the temperature of the triple point of

water."

4

Scalars and Vectors A scalar quantity has magnitude only (how much?)

Examples Mass Volume Distance Speed

A vector quantity has magnitude and direction Examples

Displacement Velocity Acceleration Force

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Aristotle’s Universe(Geocentric) Aristotle proposed that the

heavens were literally composed of concentric, crystalline spheres to which the celestial objects were attached.

Each object rotated at different velocities, with the Earth at the center.

The ordering of the spheres to which the Sun, Moon, and visible planets were attached are shown to the right.

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Stellar Parallax Stars should appear

to change their position with the respect to the other background stars as the Earth moved about its orbit, because they are viewed from a different perspective.

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Planetary Motion Most of the time, planets

move from west to east relative to the background stars. This is direct motion.

Occasionally, however, they change direction and temporarily undergo retrograde motion before looping back.

(retrograde-moveretrograde-move)

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Planetary Motion-2 Retrograde motion was first

explained using the following model devised by Ptolemy:

The planets were attached, not to the concentric spheres themselves, but to circles attached to the concentric spheres, as illustrated in the adjacent diagram.

These circles were called "Epicycles",and the concentric spheres to which they were attached were termed the "Deferents".

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Planetary Motion-3

In actual models, the center of the epicycle moved with uniform circular motion, not around the center of the deferent, but around a point that was displaced by some distance from the

center of the deferent.

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Heliocentric Model Copernicus proposed that

the Sun, not the Earth, was the center of the Solar System. Such a model is called a heliocentric system.

The ordering of the planets known to Copernicus in this new system is illustrated in the following figure, which we recognize as the modern ordering of those planets. (copernican-move)

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Galileo Galilei

Galileo used his telescope to show that Venus went through a complete set of phases, just like the Moon. This observation was among the most important in human history, for it provided the first conclusive observational proof that was consistent with the Copernican system but not the Ptolemaic system.

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Kepler- Elliptical orbits

The amount of "flattening" of the ellipse is the eccentricity. In the following figure the ellipses become more eccentric from left to right. A circle may be viewed as a special case of an ellipse with zero eccentricity, while as the ellipse becomes more flattened the eccentricity approaches one.

(eccentricity-anim)

13

Kepler’s Laws

Kepler’s 1st Law:

The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.

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Kepler’s Laws

Kepler’s 2nd Law:

The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.

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Kepler’s Laws

Kepler’s 3rd Law:

The ratio of the squares of the revolution periods (P) for two planets is equal to the ratio of the cubes of their semimajor axes (R).

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Speed

“How fast/ How slow is it going?”

Time rate of change of motion:Time rate of change of motion:

Speed = Speed = distance distance timetime

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Constant Motion vs. Changing Motion Object’s motion is Object’s motion is constantconstant: :

its speed and direction are its speed and direction are not not changingchanging

Object’s motion is Object’s motion is changingchanging:: its speed and/ or direction are its speed and/ or direction are changingchanging

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Acceleration

“Is it speeding up, is it slowing down, How fast is its speed changing?”

More important:More important:

““How is its motion changing?”How is its motion changing?”

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Acceleration (con’t)Acceleration = change in velocity

time

a = a = vvff - -

vvii

t tor or a = a = v v

t t

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. . .. . .

~ how an object’s velocity changes depends on air ~ how an object’s velocity changes depends on air resistanceresistance

~ an object’s velocity increases as it falls~ an object’s velocity increases as it falls

. . .. . .

Acceleration Due to Gravity

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Motion with Constant Acceleration

Recall: a = vf - vi

t

. . .. . .

vvff = a t = a t andand d = ½ atd = ½ at22

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Motion in a Circle Recall that acceleration is defined as a

change in velocity with respect to time. Since velocity is a vector quantity, a

change in the velocity’s direction , even though the speed is constant, represents an acceleration.

This type of acceleration is known as Centripetal acceleration

ac = v2/r

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Force & Motion

Force everyday words: Push or Pull

Forces are VectorsForces are Vectors

Examples:Examples:

(Earth’s Gravity pulls down on (Earth’s Gravity pulls down on objects)objects)

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Recognizing Forces

Note: The Force due to Gravity is always pulling down on us!

At-a-Distance Forces & Contact At-a-Distance Forces & Contact ForcesForces

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Net Force:The sum of all the forces

acting on an object

Net force Net force zero:zero:

Net force non-Net force non-zero:zero:

Balanced Balanced forcesforces

Unbalanced Unbalanced forcesforces

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Newton’s Laws of Motion

Net Force Net Force Change in Motion Change in Motion

(Net) force causes (Net) force causes change in motionchange in motion

Cause Cause EffectEffect

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Newton’s 1st Law of Motion: The Law of Inertia

An object at rest,An object at rest,

will stay at rest,will stay at rest,

unless a net, external force acts on it.unless a net, external force acts on it.

or in motion,or in motion,

will continue in the same (straight –line) will continue in the same (straight –line) motion,motion,

unbalanceunbalancedd

outsideoutside

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Newton’s 3rd Law of Motion

Better!:For every force one object exerts onto another, there is an equal & opposite force exerted back.

““For every action -For every action - there is an equal and opposite reaction.” there is an equal and opposite reaction.”

Warning: This popular expression of

Warning: This popular expression of

Newton’s 3rd Law can lead to confusion!!!!

Newton’s 3rd Law can lead to confusion!!!!

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Newton’s 2nd Law of Motion

F = ma

Force = mass x accelerationForce = mass x acceleration

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Relationship between Mass & Weight

Weight is the force due to gravity on an object

w = Fw = Fgg = ma= magg

w w = m= mgaagg

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Momentum Product of the mass and velocity of an

object

Momentum = mass x velocity

p = mv

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Conservation of Momentum When two objects collide

Law of Conservation of Linear Momentum:The total linear momentum of an isolated system remains the same: if there is no external, unbalanced force acting on the system.

(exerting forces on each other), their total momentum is conserved

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Conservation of Angular Momentum

Law of Conservation of Angular Momentum

The angular momentum of an object remains constant,

if there is no external, unbalanced torque acting on it.

Angular Momentum: The momentum of rotation

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Gravity

Does the rotation of the Earth cause gravity?

Is there gravity on the Moon? On the Sun?Is there gravity on the Moon? On the Sun?

Does the Moon’s orbit about the Earth cause Does the Moon’s orbit about the Earth cause gravity? gravity?

Does the our atmosphere/ air pressure push us Does the our atmosphere/ air pressure push us down to keep us on the ground?down to keep us on the ground?

Are the astronauts in the space shuttle really Are the astronauts in the space shuttle really weightless? weightless?

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Law of Gravity:

Every mass in the universe attracts (and is attracted by) every other mass in the universe

by a force that we call the force of gravity.

Equation form of this law:

221

r

mmGF

(where G = 6.67 x 10(where G = 6.67 x 10-11-11 Nm Nm22/kg/kg22))

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Weightlessness

(Sometimes called “microgravity”)

Apparent weightlessness: the sensation you experience when there is no floor pushing up on you.

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Work the process by which energy is transferred or

changed from one form into another

“It takes energy to do work”

Work is done when you apply a force over a distance

W = F x d

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Gravitational Potential Energy:

- the energy an object has because of its location (in a force field) “position energy”

Energy sugar in muscles PotentialEnergy of ballWork

Work I did lifting= PEball

F d = PEmaggPE = mgh

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Kinetic Energy, KE

- the energy an object has because of its motion “moving energy”

KE = ½ mv2

Work I do pushing KineticEnergy of ball

Ex: Basketball Ball

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Law of Conservation of Mechanical Energy In the absence of friction:

the sum of the kinetic energy and the potential energy of a system is constant.

(I.e., total energy is constant!)

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Power

Power = work time

P = W

t

- time rate of energy usage“How fast was the work done?”

Units: Watts = Joule/sec

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Thermal Energy (Heat) Heat is simply thermal energy; i.e., a measure

of the kinetic energy of the atoms or molecules that make up a substance.

Heat Energy is measured in calories—defined as the heat required to raise 1 gram of water by 1 o C.

The mechanical equivalent(in joules) of a calorie is : 1 calorie = 4.186 Joules

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Mass EnergyEvery object contains the

(mass)potential energy equivalent :

E = m c2

where c is the speed of light c = 3 x 108 m/s

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Relativity RevealedRelativity Revealed

11′ Lecture:′ Lecture:

The The Special Theory of Relativity Special Theory of Relativity tells us that time, distance and tells us that time, distance and mass are not what we think they mass are not what we think they are.are.

The The General Theory of RelativityGeneral Theory of Relativity shows us that mass warps space.shows us that mass warps space.

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Relativity RevealedRelativity Revealed

Special TheorySpecial Theory

Applies to non-accelerated Applies to non-accelerated “frames of reference.”“frames of reference.”

Makes two (2) assumptions:Makes two (2) assumptions:1.1. The is The is no preferred inertial frameno preferred inertial frame of of

reference.reference.

2.2. The velocity of light, The velocity of light, c is a constant.c is a constant.

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Relativity RevealedRelativity Revealed

What about assumptions?What about assumptions?

1.1. No preferred inertial frame.No preferred inertial frame.

2.2. Speed of light is constant.Speed of light is constant.

(c = 300,000,000 m/s)(c = 300,000,000 m/s)

O.K. ☑??????

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Relativity RevealedRelativity Revealed

It’s everywhere! It’s everywhere!It’s everywhere! It’s everywhere!

The Lorentz Factor:The Lorentz Factor:

1/1/√[1 - v √[1 - v 22/c /c 22 ] ]Not important until v ≈ c, then Not important until v ≈ c, then

VERY important.VERY important.

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Fundamental Principles of Temperature & Heat

• Heat energy naturally “flows” from warmer parts to cooler parts of a system

• Matter is made up of particles

and these particles are in motion

• Conservation of (Heat) Energy

(First Law of Thermodynamics)

Heat Energy lost + Heat Energy gained = 0

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• Particles are colliding with each other & the walls of the container!

• Particles are moving in all directions!

“Particles are in motion”

Microscopic Properties of Substances

Temperature, T, is a relative measure of the average KE of the particles.

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Heat Transfer Mechanisms

1. Conduction: Transfer of heat by individual particles colliding with each other

3. Radiation: Heat transfer by the absorption or emission of EM radiation (mainly infrared radiation)

2. Convection: Transfer of heat by the large scale movement of heated regions of a fluid to cooler regions

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Measuring HeatHeat energy , Q:

- thermal energy that is transferred between objects at different temperatures

“Heat flow”

Units

joules (J)

or calories (cal)

What happens when something “gains” or “loses” heat?: 1. Temperature can change or 2. Phase can change

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Heat energy must be “lost” or “gained”

c = specific heat capacity of substance

Q = mcT

T = change in temperature

m = mass

1. To change Temperature of a substance:

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Heat & Changes of Phases

Heat energy must be given off or absorbed

Q = mL

2. To change the Phase of a substance:

Lv = Latent Heat of Vaporization

Lf = Latent Heat of Fusion

Liquid - gas changes:

Solid – liquid changes:

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Phase Change Chart

Heat added

Tem

pera

ture

(ºC

)

0

20

40

60

80

-20

100

120

Ice is meltingIce & Water

Wat

er is

gainin

g heat

Water is boiling

Water & Vapor

Water only

Vapor only

Ice only

Ice is gaining heat

Vap

or is

ga

inin

g he

at

During phases changes, temperature is constant!

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2nd Law of ThermodynamicsOne statement of the Second Law of Thermodynamics:

Heat does not spontaneously flow from a low-temperature region to a high-temperature region.

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2nd Law of Thermodynamics

It is not possible to make a heat engine whose only effect is to absorb heat from a high-temperature region and turn all that heat into work.

Another form of the Second Law of Thermodynamics

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2nd Law- ContinuedIf we could design such a 100% efficient heat engine, we could then use that heat engine to power a refrigerator.

The net result of that combination would be to cause heat to flow from a cold temperature to a high temperature.

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Electricity

Electric Charge, q

Recall Structure of the Atom:

q (one proton) = + 1.6 x 10-19 C

q (one electron) = - 1.6 x 10-19 C

[Unit: coulomb, C]

Nucleus : Positively charged

Electrons: Negatively charged

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Electric Field:

The region of space around an electric charge

Coulomb’s Law

The force law that describes: charge-charge interaction

F=kQq/r2

“Like charges repel/ unlike charges attract”

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Ohm’s Law:

voltage = current x resistance

Voltage is proportional to current

V = IR

I = V/R

R = V/I

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Series circuits:

The current must flow through the resistors one at a time.

Therefore:

• Current is the same throughout the circuit.

• When one resistor breaks the current can no longer flow through any of the resistors.

Circuit with one path.

• The total resistance in the circuit is the sum of the individual resistances.

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Parallel circuits:

The current splits to flow through the resistors.

Therefore:

• The same voltage is provided to each path of the circuit.

• When one device/ resistor is turned off, or breaks, the current can continue to flow through other paths.

Circuit with many paths.

• The total current in the circuit is the sum of the currents in each path.

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Power, PRecall: Power is the time rate of energy usage P = E/t

Electric Power = current x voltage

P = IV

[Units: watt, W]

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“Like poles repel, Unlike pole attract”

Magnetism

Direction

• Ferromagnetic Materials

Just what makes a ferromagnetic material magnetic?

• Magnetic Force Field

Strength

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Electromagnetism

A moving charge creates a magnetic field Example: The Electromagnet - coils of

current carrying wire producing a magnetic field

A magnetic field can exert a force on a moving charge

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Electromagnetic Induction

The induction of an electric current in a wire when a nearby magnetic field changes

Example: The Hand-held Flashlight

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Electromagnetic Devices:

1. Motor:

2. Generator:

A device that converts electrical energy into mechanical energy

A device that converts mechanical energy into electrical energy

3. Transformers:

A device that increases or decreases the voltage of an alternating current

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Wave Types

Longitudinal Wave:A wave which consists of a series of compressions and expansions disturbances of a medium.

Transverse Wave:A wave which consists of a series of “up and down” disturbances of a medium.

Examples: Slinky

Examples: Water waves

Sound waves

Rope waves Light waves

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Wave Characteristics

Amplitude - the ‘height’ of the wave, the distance from equilibrium to the maximum displacement of the wave

• WavelengthWavelength, , the distance between corresponding points on a wavethe distance between corresponding points on a wave

• Frequency, Frequency, the number of wave disturbances that occur per secondthe number of wave disturbances that occur per second

• Wave speed, vWave speed, v the speed of the wave: the speed of the wave: vv = =

Longitudinal Waves

Longitudinal Waves

WavelengthWavelength

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Constructive Interference

http://www.colorado.edu/physics/2000/applets/fourier.html

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Destructive Interference

http://www.colorado.edu/physics/2000/applets/fourier.html

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Standing Waves

http://home.a-city.de/walter.fendt/physengl/stlwaves.htm

A standing or stationary wave is produced when two waves of the same wavelength but travelling in opposite directions interfere constructively

Longitudinal Wave

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Electromagnetic Waves

Electromagnetic waves are produced by an oscillating or accelerated charge

The changing electric field produces a changing magnetic field

http://www.phy.ntnu.edu.tw/~hwang/emWave/emWave.htmlhttp://home.a-city.de/walter.fendt/physengl/emwave.htm

http://www.Colorado.EDU/physics/2000/applets/fieldwaves.html

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Doppler Effect

http://home.a-city.de/walter.fendt/physengl/dopplerengl.htm

A change in pitch resulting from the relative motion of the source of the sound and the observer.When a source of sound is moving toward you, the wave crests are closer together and the pitch sounds higher. When the source of sound is moving away from you, the wave crests are farther apart and the pitch sounds lower.

http://www.mohawk.net/~viking/physics/doppler.html

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Electromagnetic Radiation

81

Radio Waves-- Amplitude Modulation

http://www.colorado.edu/physics/2000/applets/fourier.html

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Infrared Radiation

Light whose wavelength is longer than visible light

“Heat” Radiation-- produced by objects whose temperature is ~ 300 K

83

Ultraviolet Radiation

Light whose wavelength is shorter than visible light

Higher in energy than visible light--produces damage in organic material (e.g., sunburn)

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X-Ray Radiation

Electromagnetic radiation of short wavelength and high-energy. Produced by rapid deceleration of electrons or other high energy processes

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Gamma Ray Radiation

The highest energy, shortest wavelength electromagnetic radiation. Produced by nuclear decay or highly energetic processes.

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Structure of the AtomFor at least 25 centuries, matter believed

to be made of tiny particles -- atoms.Newton thought that atoms were hard and

indivisible. Complex structure of the atom not

observed until 20th century. In 1897, J.J. Thomson discovered the

electron. In 1911, Ernest Rutherford detected the

atomic nucleus.

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Bohr Model of the Atom “Planetary model” of the atom.

Neutrons and protons occupy a dense central region called the nucleus.

Electrons orbit the nucleus much like planets orbiting the Sun.

Modifications Only certain select radii are possible for

the electron orbits. If an electron moves in an allowed orbit, it

radiates no energy. The amount of energy required to move from

one orbit to another is fixed.

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Photon: A particle of light• The photon is a unit packet of electromagnetic radiation

• The photon has an energy that depends on its frequency:

E = h (h = 6.626 x 10-34 Js)

The energy of one photon!

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Photons Electrons may exist only in orbitals having

certain specified energies. Atoms can absorb only specific amounts of

energy as their electrons are boosted to excited states; atoms emit only specific amounts of energy when their electrons fall back down to lower energy states.

The light absorbed or emitted must be in “packets” of electromagnetic radiation containing a specific amount of energy.

These packets are called PHOTONS. The energy of a photon is related to the frequency

of the electromagnetic energy absorbed or emitted.

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Waves in generalWaves in general LightLight

Frequency and Energy Frequency is very important in physics and in astronomy,

where we are very often interested in such things as energy and temperature.

This is because energy is related to the frequency of light by

E = hf E = hf E = h E = h

When writing about light, people often use the Greek symbol (pronounced “noo”) for frequency, and c for the speed of light.

So in astronomy you will often see the symbols and c for frequency and speed.

c = c = v = fv = f

E = hf E = hf h = Planck’s constanth = Planck’s constantwhere

91

Three Types of Spectra

92

Emission Spectra

Pattern of bright spectral lines produced by an element.

93

Photoelectric effect

94

95

Band of Stability

Chart of the Isotopes

As the atomic number increases, more neutrons are needed to make the nucleus stable

Clues to radioactivity:

Atomic number of 83 and above

Fewer neutrons than protons in the nucleus

Odd-Odd nuclide

96

U-238 Decay

PoRn

RnRa

RaTh

ThU

UPa

PaTh

ThU

21880

22284

22284

22688

22688

23090

23090

23492

23492

23491

23491

23490

23490

23892

97

Nuclear Fission

When a nucleus fissions, it splits into several smaller fragments.

Two or three neutrons are also emitted.

The sum of the masses of these fragments is less than the original mass.

This 'missing' mass (about 0.1 percent of the original mass) has been converted into energy.

Fission can occur when a nucleus of a heavy atom captures a neutron, or it can

happen spontaneously.

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Fission-Continued...

A chain reaction occurs when neutrons released in fission produce an additional fission in at least one further nucleus. This nucleus in turn produces neutrons, and the process repeats.

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Control of Fission

To maintain a sustained controlled reaction, for every 2 or 3 neutrons released, only one must be allowed to strike another uranium nucleus. Nuclear reactions are controlled by a neutron-absorbing material, such as cadmium or graphite.

100

Nuclear Fusion

Fusion is combining the nuclei of light elements to form a heavier element.

In a fusion reaction, the total mass of the resultant nuclei is slightly less than the total mass of the original particles.

101

Fusion

In order for fusion reactions to occur, the particles must be hot enough, in sufficient number and well contained.

These simultaneous conditions are represented by a fourth state of matter known as plasma.

In a plasma, electrons are stripped from their nuclei. A plasma, therefore, consists of charged particles, ions and electrons.

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Fusion

Magnetic confinement utilizes strong magnetic fields, typically 100,000 times the earth's magnetic field.

Inertial confinement uses powerful lasers or high energy particle beams to compress the fusion fuel.

The enormous force of gravity confines the fuel in the sun and stars.

103

Nuclear Scales

104

Nuclear Scales--cont.

105

Fundamental Particles

106

Fundamental ParticlesQuarks make up protons and neutrons, which, in turn, make up an atom's nucleus.

Each proton and each neutron contains three quarks.

There are several varieties of quarks, as seen to the right.

Protons and neutrons are composed of two types: up quarks and down quarks.

The sum of the charges of quarks that make up a nuclear particle determines its

electrical charge.

107

Building an AtomProtons contain two up quarks and one down quark.

+2/3 +2/3 -1/3 = +1

Neutrons contain one up quark and two down quarks.

+2/3 -1/3 -1/3 = 0

The nucleus is held together by the "strong nuclear force," which is one of four fundamental forces

The strong force counteracts the tendency of the positively-charged protons to repel each other. It also holds together the quarks that make up the protons and neutrons.

http://cgi.pbs.org/wgbh/aso/tryit/atom/

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Antimatter

Antimatter is matter with a charge opposite to that of what we think of as normal matter, such as: Electron, Positron, Proton, Anti-proton, and Neutron, Anti-neutron, etc.

Antiparticles act in much the same way as do ordinary particlesEach has the same mass as their counterparts, but the charge is opposite.

If any particle touches it's corresponding antiparticle both would be totally annihilated leaving only energy.