Download Physics Chapter 22 Notes New book Atoms are composed of

Physics Chapter 22 Notes New book
Atoms are composed of protons, neutrons and electrons (except for Hydrogen, which has no neutron).
Protons and neutrons of an atom are called nucleons. Due to the fact that the nuclei of atoms are really
small, usually about 10 -15 m, the femtometer, fm, or Fermi is 10- 15m is used to describe sizes of atoms.
27
Al
For Aluminum, the
mass number, A, is 27.
This is the total number
of nucleons in the
nucleus.
For Aluminum, the
atomic number, Z,
represents the number
of protons in the
nucleus.
For aluminum, the
neutron number is
determined by
subtracting the Z
number from the A
number= 14 n
1
2
3
H
(hydrogen)
H
(deuterium or heavy
hydrogen)
H
(tritium or heavy heavy
hydrogen)
1
1
13
A
X
Z
1
Nuclei, being composed of protons and neutrons have about the same density for every element: 2.3 EE
17 kg/m 3 .
Because electrons are so tiny, only the protons and neutrons are counted in the mass of the atom. The
protons are called unified mass units or atomic mass units (amu). Electrons are about 2000 times lighter
than protons.
Isotopes are different flavors of an element which are different because they have different numbers of
neutrons. For instance, Carbon-12 has 6 neutrons and Carbon-14 has 8 neutrons.
If like charges repel, then why do nuclei, loaded with positive particles (protons) remain together; why
do they not fly apart? There is something called a strong force that binds nucleons together in the
nucleus. The strong force overcomes the repulsive force of the protons and keeps the nucleus compact.
The strong force is the same for protons or neutrons (it is independent of charge) and is limited to
distances of 10-15 m. Distances greater than 10-15 m are out of the reach of strong forces.
Neutrons help keep nuclei stable. Heavy nuclei are only stable when they have more neutrons than
protons. For a Z number greater than 83, the repulsive forces between protons cannot be compensated
by the addition of more neutrons. Elements that contain more than 83 protons do not have stable
nuclei. In real life, unstable nuclei decay until they become stable.
CH 22 Subatomic Physics Dr. Barnes
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The binding energy is the energy released when unbound nucleons come together to form a stable
nucleus, which is equivalent to the energy required to break the nucleus into individual nucleons.
Conversion of 1 u of mass into energy would produce about 931.9 MeV.
The mass of the nucleons when unbound minus the mass of the nucleons when bound is called the mass
defect. Weirdly, the mass of a nucleus is smaller than the mass of the sum of all of the individual
protons and neutrons combined.
The mass of the unbound nucleus is equal to the sum of the individual nucleon masses and the mass of
the bound nucleus is about equal to the atomic mass minus the mass of the electrons.
The binding energy for elements with an atomic number less than 20 is smaller than for those elements
with more protons. The average binding energy per nucleon is about 8 MeV for elements greater than
atomic number 20. So, the bigger the element, the more energy is takes to hold it together.
Atoms that are not stable break apart. The process of an atom breaking apart is called nuclear decay.
The decay may be spontaneous or artificially induced and usually energy is released in the form of
particles, photons or both. The emission o f particles and photons is called radiation and the process is
called radioactivity. The nucleus before decay is called the parent nucleus and the nucleus remaining
after decay is called the daughter nucleus. In all nuclear reactions, the energy released is measured with
the formula E = mc2.
There are three types of decay that can be emitted by a nucleus as it undergoes radioactive decay:
alpha, beta and gamma radiation.
In alpha decay, the emitted particles are helium nuclei. A helium nucleus involves a mass loss with a
new element produced. A helium nucleus has a composition of 2 protons and 2 neutrons and has a
charge of +2. Alpha particles can usually be stopped by a piece of paper.
238
92
U->
234
Th
90
+
4
He
2
Rules for nuclear decay:
The total of the atomic numbers on the left is the same as the total on the right because the charge
must be conserved.
The total of the mass numbers on the left is the same as the total on the right because nucleon number
must be conserved.
CH 22 Subatomic Physics Dr. Barnes
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Beta decay involves the loss of electrons or positrons (positively charged particles with a mass equal to
that of the electron). Electrons are -1 and positrons are +1, but the loss of either involves no change in
mass number because neither are considered to have a significant mass. Beta decay, however can
result in a new element formed. Beta decay can penetrate a few millimeters of aluminum.
14
C
6
12
14
N
+
7
N
7
12
0
e (electron lost)
-1
C
+
6
0
e (positron lost)
1
Beta decay transforms neutrons and protons:
1
n
0
1
1
1
p
+
1
p
1
0
0
e
-1
n
+
0
e
1
In the Carbon-14 equation listed earlier, it was noticed in the mid-1900’s that energy is not conserved in
this equation. Pauli reasoned that there must be another particle, a neutrino, involved in this decay
which would account for the disparity in energy conservation in the decay of Carbon-14. The Greek
letter nu (v) is used to represent a neutrino. When a bar is drawn above the nu, an antineutrino or the
antiparticle of a neutrino is represented. The neutrino has no electric charge and its mass is very small.
Due to this discovery, the rule is: In beta decay, an electron is always accompanied by an antineutrino
and a positron is always accompanied by a neutrino.
CH 22 Subatomic Physics Dr. Barnes
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14
C
6
12
14
N
+
0
7
N
7
12
e
+
bar nu
e
+
nu
-1
C
+
0
6
1
Gamma radiation is composed of high energy photons with a release of energy only. Gamma rays can
penetrate several centimeters of lead.
Gamma rays often result from an alpha or beta decay in which the nucleus becomes more excited. It
releases energy in the form of a gamma ray to return to its ground state. In gamma decay, energy is
emitted but the parts of the nucleus are left unchanged.
Nuclear reactions:
Any process that involves a change in the nucleus of an atom is called a nuclear reaction. Nuclear
reactions include fission, in which a nucleus splits into two or more lighter nuclei and fusion, in which
two or more nuclei combine.
For fission to occur to occur naturally, the nucleus must release energy. The nucleons in the daughter
nuclei must be more tightly bound and therefore have less mass than the nucleons in the parent
nucleus. This decrease in mass appears as released energy in the form of photons or kinetic energy.
Since fission produces lighter nuclei, the binding energy per nucleon must increase with decreasing
atomic number. This is only possible for atoms in which A>58. Fission, therefore only occurs with heavy
atoms.
Below is a typical fission reaction caused by bombarding an Uranium with a neutron.
1n
0
+
235U
92
->
140Ba
56
+
93Kr
+
36
3
1n
0
Notice how the numbers balance from side-to-side in the equation.
The energy released in the fission of one atom is about 100 million times the amount released in a single
molecule of gasoline (octane).
CH 22 Subatomic Physics Dr. Barnes
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When Uranium-235 undergoes fission, the extra neutrons released can cause a chain reaction if the
reaction is uncontrolled. If the energy in 1 kg of Uranium-235 were released, it would equal the energy
in about 20,000 tons of TNT. This is the idea behind nukes. The original atomic bomb dropped by the
USA on Japan in 1945 was a tremendous nuclear fission reaction.
Nuclear reactors are designed to maintain a controlled, self-sustained chain reaction, for the production
of energy. At this point, all nuclear reactors are fission reactors. Bad news: The radioactive by-products
of nuclear energy have half-lives of 10,000 years or longer.
Nuclear fusion occurs when two light nuclei combine to form a heavier nucleus. As with fission, the
product of a fusion event must have a greater binding energy than the original nuclei for energy to be
released. Since the binding energy per nucleon must increase as atomic number increases, atomic
fusion only occurs for atoms with atomic numbers less than 58. Because water is plentiful, it is
considered the preferred fuel for future fusion reactors. The chief problem with a controlled fusion
process is that to impart enough kinetic energy to the nuclei, the fuel must be heated to about 10 8 K or
about 10 times greater than the interior temperature of the sun. That’s really hot and very expensive.
The fusion reaction in 90% of stars fuse hydrogen and probably helium. The released energy is carried
by gamma rays, positrons, and neutrinos. The energy-liberating fusion reactions are called
thermonuclear fusion reactions. The hydrogen or fusion bomb was first detonated in 1952.
Particle physics is all about discovering the ultimate structure of matter: elementary particles.
Following is an explanation called the standard model. Elementary particles do not appear to be
divisible and have neither size nor structure. Originally, it was thought that electrons and protons were
the fundamental particles. Since 1945, over 300 new particles have been catalogued in the search for
this grail.
The four fundamental interactions of particles include: strong, electromagnetic, weak and gravitational.
All of these interactions are mediated by particles and are categorized in broad categories: leptons and
hadrons. The only particle of the four forces following that has not been detected is the graviton.
The strong interaction is responsible for binding protons and neutrons in the nucleus. The strong force
is the “glue” that holds that holds the nucleons together. The strong force is very short-ranged and is
negligible for separations greater than about 10-15 m (the approximate size of a nucleus). The strong
interaction is mediated by gluons.
The electromagnetic interaction is about 1/100 the strength of the strong interaction, is responsible for
the attraction of unlike charges and the repulsion of like charges. It is a long-range interaction that
decreases in strength according to the inverse square rule. The electromagnetic force is mediated by
photons.
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The weak interaction is a short-range that is involved in beta decay. It is about 10-13 times the
interaction of the strong force. The weak interaction is mediated by W and Z bosons.
The gravitational attraction is a long-range interaction with a strength of only about 10-38 that of the
strong interaction. It holds solar systems and galaxies together but is real weak on the subatomic level.
The gravitational attraction is proposed to be mediated by gravitons.
Hadrons are particles that participate in the four interactions, but leptons participate in all forces except
the strong force. Electrons and neutrinos are both leptons. Leptons have no measurable size and do
not seem to break down into smaller units; therefore, leptons appear to be truly elementary. The six
leptons are: electron, muon, tau, each paired with a neutrino. Each of the six leptons has an
antiparticle.
Hadrons can be divided into mesons and baryons. Baryons are protons and neutrons, which compose
everyday matter. Mesons are unstable and are not part of ordinary matter. Hadrons are thought to be
composed of charged quarks (fractionally) which are in pairs (up and down, top and bottom and charm
and strange). Associated with each quark is an antiquark of opposite charge.
Mesons are composed of one quark and one antiquark. Baryons are composed of three quarks.
Antibaryons are composed of three antiquarks.
Despite many efforts, no isolated quark has ever been observed. Some physicists believe that quarks
are permanently confined inside ordinary particles by the strong force. This is called the color force,
which is the property of quarks that allows them to attract one another and form composite particles.
It is thought that up until 3-7 x 105 years after the big bang, most of the energy in the universe was in
the form of radiation rather than matter. Evolutionists believe that matter resulted as the energy
cooled after the initial explosion.
CH 22 Subatomic Physics Dr. Barnes
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22A Binding energy
The nucleus of the deuterium atom, called the deuteron, consists of a proton and a neutron. Given that
the atomic mass of deuterium is 2.014102 u, calculate the deuteron’s binding energy in MeV.
Atomic number = Z 1
1
H
Mass number = A
A 1
H
1.007
2.104
2
H
Z 1
H
1
atomic mass of deuterium = 2.014102u
atomic mass of H
Z
=
1
N
=
1
=
1.007825u
CH 22 Subatomic Physics Dr. Barnes
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mn
=
1.008665u
c
=
3.00
Ebind
=
?
Ebind
=
Δmc2
Binding energy =
x
108 m/s
mass defect
x
(speed of light)2
The energy of 931.48MeV/u can be substituted for c2 in the equation above.
M
=
Z(atomic mass of H)
+
Nmn
-
atomic mass
M in the equation above is mass defect. The total mass of a stable nucleus (mbound) is always less than
the sum of the masses of its individual nucleons (munbound). Mn is the mass of a neutron.
Ans: In order for a deuteron to be separated into its constituents-a proton and a neutron-2.224MeV of
energy must be added.
CH 22 Subatomic Physics Dr. Barnes
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22B Nuclear Decay
The element radium was discovered my Marie and Pierre Curie in 1898. One of the isotopes of radium,
226
Ra
88
decays by alpha emission. What is the resulting daughter element?
Hint: show a Helium nucleus on the right side of the equation
4
He
2
Ans:
226
88
Ra -> 222
86
Rn
+
4
He
2
(find the new element in Appendix G of your book)
CH 22 Subatomic Physics Dr. Barnes
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22C Measuring nuclear decay
The half-life of the radioactive radium (226Ra) is 5.0 x 1010 s.
A sample contains 3.0 x 1016 nuclei.
What is the decay constant for this decay?
The half-life for a nucleus is:
T1/2
=
0.693
λ
Half-life =
0.693
Decay constant
First find wavelength:
λ=
0.693
=
0.693
=
1.4 X 10-11/S
5.0 x 1010 s
T1/2
How many radium nuclei, in curies, will decay per second?
Activity=λN
=
1.4 x 10-11
x
3.0 x 1016 nuclei =415800 nuclear decays
S
s
One curie (Ci) is equal to 3.7 x 1010 decays/second.
415,800 decays
S
x
1 curie
=
.000011 Ci
3.7 x 1010 decays
CH 22 Subatomic Physics Dr. Barnes
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S
CH 22 Subatomic Physics Dr. Barnes
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