Download lecture 3

Classroom notes for:
Radiation and Life
98.101.201
Professor: Thomas M. Regan
Pinanski 207 ext 3283
Class 3: Units and Measures
 Derived Quantities
– Oftentimes when numerically evaluating our
observations to explain the natural world, it is necessary
to perform mathematical operations on quantities to
properly express their relationships.
– Derived quantities result when mathematical operations
have been performed on the fundamental (or other
derived) quantities.
Energy
 Energy is measured in N*m in SI units; or
equivalently, it can be expressed in terms of the
joule (J), also a shorthand notation.
– Energy comes in many forms: light, heat, the kinetic energy of a
moving object (kinetic energy), etc…
– To put this unit of measure in perspective, consider another unit
known as the calorie, which used in dietetics for stating the energy
(heat) content of a food, i.e., the amount of heat energy that the
food can yield as it passes through the body. One calorie = 4,185
joules in this context.
– The heat of fusion for water is approximately 333 joules/gram.
(http://www.infoplease.com/ce5/CE008611.html)
– The unit is named for the English physicist James Prescott Joule
(1818-1889).
– (http://www.encarta.msn.com)
Power
 Power is measured in J/s in SI units, or in
watts (W).
 As an example, note that a 100-watt light
bulb emanates 100 joules of infrared and
light energy each second.
 The unit is named for the Scottish engineer
and inventor James Watt (1736-1819).
 (http://www.encarta.msn.com)
Flashlight Spectral Emission 4600 K
Wien's displacement law & Stefan-Boltzmann law
Frequency
 Frequency is measured in cycles per second (1/s),
also known as the hertz (Hz).
– A cycle can be a toss of the pen from my hand to the
height of its travel and back; it can be a wave of water or
sound, etc..
– When watching water waves in a pond, the number of
wave crests that pass by each second is the frequency in
Hz.
– This unit is named in honor of Heinrich Hertz (18571894), a German physicist. (http://www.encarta.msn.com)
Unit Prefixes
 If a quantity is very large, sometimes it easier to
express it in shorthand notation. For example,
suppose you measure a distance of 1000 meters.
What is this called?
– In radiation sciences unit prefixes are important
because the numbers involved tend to be either very
large or extraordinarily small.
– Some common prefixes in the SI system are:
–
–
–
–
–
–
–
–
Numbers larger than one:
prefix
multiple
kilo
(x1,000)
mega
(x1,000,000)
giga
(x1,000,000,000)
tera
(x1,000,000,000,000)
peta
(x1,000,000,000,000,000)
exa
(x1018)
abbrev.
k
M
G
T
P
E
To understand the relative scales of these values, consider:
 one kilogram = 1,000 grams (weighs about 2.205 lb on the
earth’s surface);
 one megawatt of electricity would light 10,000 100-Watt
light bulbs;
 ½ gigameter is about the distance between the earth and
the moon (3.84 x108 m).
 Numbers smaller than one (fractions):






prefix
centi
milli
micro
nano
pico
 femto
multiple
(1/100)
(1/1,000)
(1/1,000,000)
(1/1,000,000,000)
(one trillionth)
10-15
abbrev.
c
m
m
n
p
Scientific Notation
 Scientific notation is simply another shorthand
method for writing very large or very small
numbers.
–
–
–
–
–
–
–
–
–
Numbers larger than one:
1 = 100
10 = 101
100 = 102
1,000 = 103
(kilo)
1,000,000 = 106
(mega)
1,000,000,000 = 109
(giga)
1,000,000,000,000 = 1012
(tera)
The superscript is called an exponent. For numbers larger
than one, the number is written as a “one” followed by a
number of zeroes equal to the exponent.
 Numbers smaller than one:
– 1 = 100
– 1/10 = 10-1
– 1/100 = 10-2
– 1/1,000 = 10-3
– 1/1,000,000 = 10-6
– 1/1,000,000,000 = 10-9
– 1/1,000,000,000,000 = 10-12
– 1/1,000,000,000,000,000 = 10-15
 For numbers smaller than one (fractions), the
number is written as a “one” divided by a “one”
followed by a number of zeroes equal to the
exponent. Notice that the exponent is negative for
fractions of one.
Historical Developments in Modern Physics
 “To understand a science it is necessary to know its
history.” August Comte (1798-1857), the French positivist philosopher, was a founder of sociology.
(http://www.encarta.msn.com)
 Circa 1800, we had a general understanding of the world
around us.
 Newton’s three Laws of Motion were known.
– An object at rest tends to stay at rest, an object in motion tends to
stay in motion.
– An object continues in its initial state of rest or motion with uniform
velocity unless it is acted on by an unbalanced, or net external, force.
(Physics 3rd Ed., Tipler, p. 77)
– This may seem to be a counterintuitive thought. For example, push a
book so that it slides freely along the surface of a table, and the book
will eventually come to a stop. However, this is because of friction.
If a book were thrown in the vacuum of space, it would continue to
travel forever until it hit something.
F = m*a
– F is force in Newtons,
– m is mass in kilograms, and
– a is acceleration in m/s2.
• Note that F and a are vector quantities.
 With this formula, it is demonstrated that exerting a net force
on an object will accelerate it (speed it up or slow it down).
Consider the example of throwing the book in a vacuum.
Give it a single push and it will fly through the void at a
constant speed. However, push it continuously and it will
speed up. The book sliding on the desk can’t continue to
move at a constant speed because the force of friction is
causing it to slow down.
 For every action, there is an equal and opposite reaction.
Forces always occur in pairs. If object A exerts a force on
object B, an equal but opposite force is exerted by object B
on object A. (Physics 3 Ed., Tipler, p. 78)
rd
Newton Continued
 For every action, there is an equal and opposite reaction.
Forces always occur in pairs. If object A exerts a force on
object B, an equal but opposite force is exerted by object B
on object A. (Physics 3rd Ed., Tipler, p. 78)
 The classic example of this is a rocket. It pushes away its
burning exhaust gasses, and they in turn propel it forward.
When I push on a desk or wall, it pushes back, but friction
keeps me rooted to the spot. If I did this at an ice-skating
rink, I would be pushed out into the rink.
 Newton’s theory for gravity was understood.
Essentially, Newton described gravity as a force of
attraction between any objects with mass, and was
able to formulate this mathematically.
 Although Kepler’s laws were an important step in
understanding the motion of the planets, they were
still merely empirical rules obtained from the
astronomical observations of Brahe. It remained
for Newton to take the giant step forward and
attribute the acceleration of a planet in its orbit to
a force exerted by the sun on the planet that varied
inversely with the square of the distance between
the sun and the planet. Others besides Newton
had proposed that such a force existed, but
Newton was able to prove that a force that varied
inversely with the square of the separation
distance would result in the elliptical orbits
observed by Kepler.
 Newton then made the bold assumption that such a
force existed between any two objects in the
universe (before Newton, it was not even
generally accepted that the laws of physics
observed on earth were applicable to the heavenly
bodies). (Physics 3rd Ed., Tipler, p. 299)
 There seems to be no reason to doubt the
basic truth of the story of Newton and the
apple: that in 1666, having left Cambridge
for a while on account of the Great Plague,
he was moved by the fall of an apple to
speculate if the Moon itself was falling
toward the earth in a similar way. (Physics 3 Ed.,
rd
Tipler, p. 299)
Basic theories for electricity and magnetism were known.
 Electric charge can be either positive or negative.
Two objects that carry the same type of charge –that
is, two objects that are both positive or both
negative– repel each other, and two objects that
carry opposite charges attract each other.(Physics 3 Ed.,
rd
Tipler, p. 599)
– Electric current is defined as the rate of flow of electric
charge through a cross-sectional area. (Physics 3 Ed., Tipler, p. 599)
rd
 Basic theories for optics were understood.
– Optics is the branch of physics dealing with the nature and
properties of light and vision. (Webster’s New World Dictionary, Third College
Edition)
– Newton concluded that white light was composed of a
mixture of a whole range of independent colors. (Optics, Hecht, p.
3)
Light
 There was debate as to its exact nature; some
viewed it as being made of particles, some
viewed it as a wave.
– Isaac Newton believed light to be particulate in
nature. (Optics, Hecht, p. 3)
– Christiaan (this is the correct spelling of the
name) Huygens (1629-1695) advanced the wave
theory of light. He was able to derive the laws of
reflection (the angle-of-incidence equals the
angle-of-reflection) and refraction. (Optics, Hecht, pp. 3, 97)
The Law of Conservation of Mass
 The French chemist Antoine-Laurent Lavoisier
(La-vwa-zee-ay) (1743-1794) had written a
textbook in which he stated that in any closed
system (one from which no mass was allowed to
leave, and into which no mass was allowed to
enter), the total amount of mass remained the
same no matter what physical or chemical changes
went on. (Asimov’s Chronology of Science and Discovery, Asimov, pp. 240, 266)
 Fouquier-Tinville’s notorious words during the
Revolution sent the chemist Lavoisier to the
guillotine: “The Republic does not need any
scientists.” (wysiwyg://114/http://www.nobel.se/physics/articles/curie)
Elements and Compounds
 Elements and compounds were known to exist.
– An element can be informally defined as something
with unique physical and chemical properties and
something that cannot be broken down into any other
substances. For example, gold, silver, and iron are
elements.
– A compound also is defined by its unique physical and
chemical properties, but it can be broken down into
simpler constituents (elements). For example, water
can be broken down into hydrogen and oxygen, while
table salt can be reduced to chlorine and sodium.
– Subsequent investigations proved that the smallest unit
of a chemical substance such as water is a molecule.
Each molecule of water consists of a single atom of
oxygen and two atoms of hydrogen joined.
(http://www.encarta.msn.com)
 Subsequent investigations proved that the smallest
unit of a chemical substance such as water is a
molecule. Each molecule of water consists of a
single atom of oxygen and two atoms of hydrogen
joined. (http://www.encarta.msn.com)
 The discoveries of both John Dalton (1808) and
Amedeo Avogadro (1811) were important in this
area of investigation.
– Essentially, Dalton returned to the Greek notions of
Democritus that all matter was made up of tiny,
indivisible particles. Dalton even used Democritus’
word atom for these particles. The Greeks thought that
atoms differed among themselves in shape. Dalton, in
whose time weight and measurements had grown
important, maintained that the difference was one of
weight, and he pioneered the concept of atomic weight.
(Asimov’s Chronology of Science and Discovery, Asimov, p. 287)
Avogadro
 The name "Avogadro's Number" is just an
honorary name used to describe the
calculated value of the number of atoms,
and molecules in a gram mole of any
chemical substance. It is 6.022 x 1023
atoms/mol.
Avogadro’s Number
1820
– 1820- Several discoveries that year firmly established
that moving charge (electric current in a wire, for
example) produces a magnetic field.
– As part of a classroom demonstration, Hans Christian
Oersted (1777-1851) had brought a compass needle
near a wire through which a current was passing. The
compass needle twitched and pointed neither with the
current nor against it but in a direction at right angles to
it. When Oersted reversed the direction of the current,
the needle pointed in the opposite direction but still at
right angles to the flow. (Asimov’s Chronology of Science and Discovery, Asimov, pp.
308-309)