Transcript lecture 8

Classroom notes for:
Radiation and Life
98.101.201
Professor: Thomas M. Regan
Pinanski 207 ext 3283
The Four Forces
Gravity is an attractive force that acts between all
objects with mass.
It is a 1/r2 law; that is, doubling the distance between two objects
with mass will serve to decrease the gravitational attraction
between them by a factor of four (strictly speaking, this is only
true for point masses or spherical bodies). Likewise: tripling the
distance will decrease the attraction by a factor of nine;
quadrupling the distance will decrease the attraction by a factor
of sixteen, and so on…
It is (as far as we know) always attractive.
There are theories that postulate that antigravity can exist under
conditions such as those present at the start of the universe; for
the purposes of our class we can safely discuss gravity as being
an attractive force only.
It is by far the weakest of the forces.There is no danger that the
overhead projector will ever fly at me due to gravitational
attraction.
It is by far the weakest of the forces.There is no danger
that the overhead projector will ever fly at me due to
gravitational attraction.
However, because the earth is so massive, gravity
dominates interactions between objects on a
macroscopic scale.
As a force, it is measured in newtons (kg*m/s2); the
rough equivalence is 1 N = .2248 lb.
(Physics 3rd Ed., Tipler, back cover)
It plays no role in the study of radiation and its
interactions with matter, so will rarely be mentioned
again in this class.
Electromagnetism
The electromagnetic force acts between all objects
with charge.
It is also a “1/r2“ force (strictly speaking, this is
only true for point masses or spherical bodies).
It can be either an attractive or a repulsive force;
like charges repel; unlike charges attract.
This attraction binds electrons to the atom; it is
only so strong, however.
For progressively larger atoms, the attractive force
on the electrons grows weaker for two reasons:
the force diminishes with 1/r2; and
there are other electrons between the outermost
shells and the nucleus.
 The effective nuclear charge is the positive charge
experienced by an electron from the nucleus, equal
to the nuclear charge but reduced by any shielding
or screening from any intervening electron
distribution. (General Chemistry, Ebbing and Wrighton, pp. 292-293)
 Thus, under certain circumstances, electrons can
be removed from the atom, creating ions.
 As a force, it is measured in newtons (kg*m/s2);
the rough equivalence is 1 N = .2248 lb.
(Physics 3rd Ed., Tipler, back cover)
 It plays an important role in our understanding of
radiation and its interactions with matter, so will
be mentioned again.
You can’t measure the gravitational attraction between the two
protons on opposite sides of a medium sized nucleus; however,
they are pushing each other apart with an electrostatic force strong
enough to tear the nucleus apart.
Why doesn’t the electromagnetic force dominate our daily
existence? Matter is essentially neutral, and there are very rarely
large enough charge buildups for the force to manifest itself on a
large scale. And, recalling a question posed when discussing the
discovery of the neutron: why doesn’t the nucleus explode apart
due to electrostatic repulsion? One of the other forces works to
counteract it within the nucleus.
Pair of
Separation Gravitational Gravitational Coulombic Coulombic
Objects
Distance(m)Attraction(N)Attraction(lb)Repulsion(N)Repulsion(lb)
person-person 1.00E+00 3.27E-07 7.35E-08
earth-person 6.37E+06 6.87E+02 1.54E+02
proton-proton 1.00E-14 1.87E-36 4.20E-37 2.31E+00 5.19E-01
The Weak (Nuclear) Force
The weak force is responsible for the emission of beta particles
from radioactive nuclei.
The beta-decay interaction is one of a general class of
phenomena known collectively as weak interactions. (Introductory Nuclear
Physics, Krane, p. 285)
The weak nuclear force can only act over a distance on the order
of magnitude of the nuclear size. (http://www.final.gov/pub/electroweak.html)
With respect to beta decay, the weak force is actually about
1000 times weaker than the electromagnetic force. (Introductory Nuclear
Physics, Krane, p. 285)
Weak interactions are responsible for the fact that all the more
massive quarks and leptons decay to produce lighter quarks and
leptons. When a particle decays, it disappears and in its place two or
more particles appear. The sum of the masses of the produced
particles is always less than the mass of the original particle. This is
why stable matter around us contains only electrons and the lightest
two quarks (up and down). (http://www.phy.cuhk.edu.hk/cpep/weak.html
The present theory of the weak interaction is based on an
exchange-force model. The exchanged particles are known as
intermediate vector bosons, represented by W+, W-, and Z0.
(Introductory Nuclear Physics, Krane, p. 703)
The existence of the weak bosons was proposed by S.
Weinberg and A. Salam who in 1967 separately made the first
step toward achieving a unified description of all particle
interactions by combining the electromagnetic and weak forces
into a single theoretical framework. This electroweak theory
postulates that at very high energy the weak and
electromagnetic forces become completely equivalent. The
pure electroweak force would be mediated by four massless
spin-1 particles… At lower energies, the symmetry between
weak and electromagnetic forces is broken, and three of the
four exchanged particles lose their massless character to
become the weak bosons W+, W-, and Z0. The fourth particle
remains massless and is the ordinary photon of
electromagnetism. (Introductory Nuclear Physics, Krane, pp. 704-705)
The Strong (Nuclear) Force
The strong force is an attractive force that acts between a proton and
a proton, or a neutron and a proton, or a neutron and a neutron.
(Radiation and Health, Luetzelschwab, p. A3
by (Radiation and Health, Luetzelschwab, pp. A3-A4)
far the strongest of the forces- about 100 times stronger than the
electromagnetic force.(Introductory Nuclear Physics, Krane, p. 285)
It has an incredibly short range of about one femtometer (10-15 m);
outside of that range, the force is zero. (Radiation and Health,
Luetzelschwab, pp. A2-A3)
Thus, unlike gravity and electromagnetism, it suddenly drops to zero
at a short distance from the particle, as opposed to gradually fading
with distance.
Compare the range of the strong force (one femtometer) to the
diameter of an average nucleus (ten femtometers).
The strong force therefore does not act beyond the bounds of the
nucleus; it does not manifest itself on the scale of everyday life.
It “battles” the repulsion of the protons to hold the nucleus together.
(Radiation and Health, Luetzelschwab, p. A3)
Technically, the proper way to describe this situation is to consider
the nuclear potential well, the Coulombic barrier, and quantummechanical barrier tunneling.
Why not just create a nucleus with neutrons only, or just a single
proton and varying numbers of neutrons, in which case there would
be no “battle”?
Recall our earlier example of the isotopes of hydrogen; a maximum
of two neutrons are allowed to exist in the nucleus with the single
proton. There are no isotopes of hydrogen with three neutrons
because nuclei with large imbalances between the number of protons
and neutrons will not exist very long; there are no nuclei composed
entirely of neutrons or entirely of protons.
The strong force involves the exchange of pi mesons between
nucleons. This is not a truly fundamental process, because the
nucleons and mesons are composite particles. The strong interaction
can be treated on a more fundamental basis in terms of the quark
model, in which the strong interaction between quarks is mediated
by the exchange of field particles called gluons. (Introductory Nuclear Physics,
Krane, p. 709)
In quantum chromodynamics (QCD), quarks interact by exchanging
gluons. The photons are the carriers of the electromagnetic field
exactly as the gluons are the carriers of the strong color field. What
makes the two theories so different is that the photons themselves
carry no electric charge and so are unaffected by electric fields;
gluons in contrast carry a net color, and therefore interact directly
with the quarks. That is, a quark can emit a gluon and then interact
with it and create additional gluons; a photon cannot itself exchange
photons with nearby charges. This property of gluons force QCD
into a considerable level of mathematical complexity. (Introductory Nuclear
Physics, Krane, p. 742)
As the distance between two point charges increases, the electric
field (corresponding to the density of electric field lines crossing a
unit surface area) decreases. The color field remains constant as the
distance increases (the gluon-gluon interaction forces the color field
lines into a narrow tube). As we try to separate to large distances,
the work will eventually exceed the production threshold for creation
of a quark-antiquark pair, resulting in the formation of a meson.
Thus putting energy into a nucleus in an attempt to liberate a quark
is expected to create new mesons, exactly as observed. (Introductory Nuclear
Physics, Krane, pp. 743-744)
Action at a Distance
 All four of the forces operate on the principle of “action at
a distance”; that is, the forces can act between objects even
if they are separated by vacuum.
It’s interesting to contemplate that some of history’s
greatest minds, which turn the world upside down, can end
up being the biggest defenders of the status quo.
 One way to envision this is by thinking of invisible fields,
or “lines of force” emanating from bodies.
 For instance, all objects with charge can be thought to have
an electric field surrounding them. If another charge is
brought into the presence of this charge, it will experience
a force that pushes it away or pulls it in.
 A permanent magnet can be thought to have magnetic lines
emanating from it. Observe this yourself by placing a bar
magnet directly under a sheet of paper and sprinkling iron
filings on the paper.
 A permanent magnet can be thought to have magnetic lines
emanating from it. Observe this yourself by placing a bar
magnet directly under a sheet of paper and sprinkling iron
filings on the paper.
 Another way to envision this by thinking of the forces being
transmitted by field particles that are exchanged between
objects.
 For instance, the electromagnetic force is transmitted by
photons that are exchanged between objects with charge;
think of two children on roller skates as representing two
positively charged protons that will repel each other. They
throw a basketball back and forth and are pushed apart, an
analogy to the photon, as the carrier of the electromagnetic
force, pushing the two like charges apart.
The Electromagnetic (EM) Spectrum
General Properties
 Remember from Bohr that if an electron moves from
a higher energy state (shell) to a lower, it gives off a
photon.
 Conversely, the electron can absorb a quantum and
move from a lower to a higher energy state as
described by this formula.
 Energy (E) = Einitial-Efinal= Planck’s constant (h) x
frequency of the radiation (n)
 The photon’s energy dictates into what part of the
electromagnetic spectrum it fits.
 The electromagnetic spectrum is simply the range of
all possible energies for photons.
 Photon energy is typically measured in electron volts (eV),
keV, or MeV.
 1 eV = the kinetic energy gained by a single electron
accelerated through a potential difference of 1 volt. (Radiation
Safety and Control, Volume 1, French and Skrable, p. 18)
 Remember Roentgen and Thomson’s cathode tubes; the
energy gained by the electron as it speeds from the cathode
(negative terminal) to the anode will be one electron volt if
the terminals have a one-volt difference between them.
 1 eV = 1.602 x 10-19 joules.
 This is a tiny amount of energy; a 100-watt light bulb
emanates 100 joules of heat and light energy each second.
Components of the Spectrum
The full range of the spectrum, from least energetic
to most, is:
radio waves;
The sending of signals by radio waves reached a
climax on December 12, 1901. Marconi broadcast
radio waves from the southeastern tip of England,
using balloons to lift his antenna as high as possible.
The signals were received in Newfoundland. This
day is usually considered the one on which radio was
invented, and Marconi is given credit as the inventor.
(Asimov’s Chronology of Science and Discovery, Asimov, p. 480)
www.users.mis.net/~pthrush/ lighting/incgraph.gif
microwaves;
Molecules can be made to vibrate and rotate; again, the
energy associated with either motion is quantized, and
molecules possess rotation and vibrational energy levels in
addition to those due to their electrons. Only polar molecules
can absorb a photon and make a rotational transition to an
excited state. For instance, water molecules are polar, and if
exposed to an electromagnetic wave, they will swing around,
trying to stay lined up with the alternating electric field. This
will occur with particular vigor at any one of its rotational
resonances. Consequently, water molecules efficiently and
dissipatively absorb microwave radiation at or near such a
frequency. The microwave oven (12.2 GHz) is an obvious
application. On the other hand, nonpolar molecules, such as
carbon dioxide, hydrogen, nitrogen, oxygen, and methane,
cannot make rotational transitions by way of the absorption of
photons. (Optics, Hecht, pp. 74-75)
infrared waves;
Infrared is copiously emitted in a continuous
spectrum from hot bodies, such as electric heaters,
glowing coals, and ordinary house radiators.
Roughly half the electromagnetic energy from the
sun is infrared, and the common lightbulb actually
radiates far more infrared than light. Like all warmblooded creatures, we too are infrared emitters. (Optics,
Hecht, p. 76)
Many molecules have both vibrational and rotational
resonances in the infrared and are good absorbers,
which is on reason infrared is often misleadingly
called “heat waves”- just put your face in the
sunshine and feel the resulting buildup of thermal
energy. (Optics, Hecht, p. 76)
visible light;
This is essentially the only part of the electromagnetic
spectrum that humans can see.
ultraviolet ;
Humans cannot see UV very well, because the cornea absorbs
it, particularly at the shorter wavelengths, while the eye lens
absorbs most strongly beyond 300 nm. A person who has had
a lens removed because of cataracts can see UV (l > 300
nm). In addition to insects, such as honeybees, a fair number
of other creatures can visually respond to UV. Pigeons, for
example, are capable of recognizing patterns illuminated by
UV and probably employ that ability to navigate by the sun
even on overcast days. (Optics, Hecht, p. 78)
xrays ; and gamma (g) rays
X- and gamma rays will be discussed in greater depth in the coming
lectures.
All of these travel at the speed of light (c), 3x108 m/s (“c” is
from the Latin word celer, meaning fast). (Optics, Hecht, pp. 44-45)
Wave-Particle Duality
Is electromagnetic energy best described as either a
particle or a wave?
It depends upon the experiment used to examine it.
Consider its wave-like properties.
In Energy (E) = h x n; “n” is the frequency of the
electromagnetic energy.
Frequency (measured in cycles/sec) is a property of waves.
Planck’s formula can also be written as:
In Energy (E) = h x c / l; ”l” is the wavelength of the
electromagnetic energy.
The wavelength is simply the distance between successive wave
crests. As shown by Einstein’s description of the photoelectric effect,
electromagnetic energy can also certainly be viewed as being
bundled in photons. For this class, we’ll almost always speak of
photons when we consider how radiation interacts with matter.
Understanding X-Rays
Now we can understand the puzzling properties of xrays.
– Invisible- essentially the only part of the
electromagnetic spectrum that humans can see is visible
light; all other forms of electromagnetic energy are
invisible to the human eye.
– Didn’t reflect/refract like light waves- x-rays have a
different frequency, so they behave differently.
– Couldn’t deflect them with a magnet- they are
electromagnetic energy, and as such carry no charge.
Only objects with charge are affected by magnets.
– They seemed to come from the wall of the cathode
tube- this is yet to be answered.