Transcript Slide 1

Environmental Physics
Chapter 13:
The Building Blocks of Matter
Copyright © 2008 by DBS
Introduction
Figure 13.1a: Evacuated tube used in observation of cathode rays.
Fig. 13-1a, p. 428
Figure 13.1b: Apparatus used by J. J. Thomson (1897) to measure the charge-to-mass ratio of the
electron. The evacuated tube is similar to a TV picture tube. The negatively charged particles
emitted from the cathode are deflected by either an electric field or a magnetic field. The parallel
plates connected to a battery provide the electric field. Two current-carrying coils (not shown)
produce a magnetic field perpendicular to the electric field. The sizes of the deflections, as noted on
the fluorescent screen, can be used to determine the charge-to-mass ratio of the electron.
Fig. 13-1b, p. 428
Figure 13.2: Radioactive elements may emit three types of radiation: electromagnetic radiation called
gamma rays; fast-moving electrons called beta particles; and alpha particles, which are the nuclei of
helium atoms. If radioactive material is placed at the bottom of a hole in a lead block, radiation will be
emitted through the top. If the beam passes through an electric field, it will separate into the three
types of radiation.
Fig. 13-2, p. 430
Figure 13.3: Scattering of alpha particles from a thin gold foil.
Fig. 13-3, p. 430
Figure 13.4: Aerial view of the Fermi National Accelerator Laboratory in
Batavia, Illinois, the world’s highest energy particle accelerator. The accelerator
ring is 6.3 km (3.8 miles) in circumference. Protons can be accelerated up to
99.99% the speed of light.
Fig. 13-4, p. 431
Figure 13.5: The nucleus of the carbon atom has a positive charge of 6. It is
surrounded by six electrons, arranged in two major shells. The number of protons
gives the element its atomic number.
Fig. 13-5, p. 432
Figure 13.6: Energy levels of electrons within atoms are analogous to floors in a
building. Here, one electron has been excited to a higher state by the addition of heat
to the atom.
Fig. 13-6, p. 433
Figure 13.7: Spectrum of light emitted by a gas that has been excited by electrical
discharge or heat.
Fig. 13-7, p. 434
End
• Review
Nuclear Structure
• Atoms are extremely small
10000 x smaller
Nuclear Structure
Particle
Symbol
Charge
Mass (amu)
Electron
Proton
Neutron
ep+
n0
-1
+1
0
0.000544 (1/1837)
1.007277
1.008665
If e- had mass of an orange (100g),
a proton would weigh 180 kg (several sacks of potatoes)
Nuclear Structure
•
•
Isotopes – atoms of the same element with different atomic masses
Same chemical properties
Mass: 1 amu
Most abundant
Mass: 2 amu
‘heavy water’
Figure 13.8: Isotopes of hydrogen.
Mass: 3 amu
Radioactive
Nuclear Structure
Z often omitted
since can be
obtained from X
Z & N referred to
as nucleons
Nuclear Structure
•
e- held in the atom by electrostatic force of attraction
•
Nucleus held together by strong nuclear force
– Short range
– >>> electrostatic force
Chemistry – changes in e-
Nuclear physics – changes in p+ and n0 via decay,
fission and fusion
Nuclear Structure
•
•
Atomic no. (Z) defines the element, chemical properties
Isotopes of the same element have the same number
of p+, but different numbers of n0
(and therefore different masses)
e.g. carbon-12 and carbon-14
Radioisotope and radionuclide are used to denote
unstable, radioatcive isotopes
Question
Radon-222 gas is formed from the radioactive decay of radium-226. It enters cracks in
basement floors and is the second leading cause of lung cancer
1. Symbolize the isotope in the form
A X
Z
2. Give the number of p+, n0 and e- in an atom of radon-222
Radioactivity
•
•
•
Radioactive nuclide is a nuclide that spontaneously undergoes nuclear decay
Results in emission of radiation (particles or rays)
3 types of radiation: alpha, beta and gamma
Figure 13.2: Radioactive elements may emit three types of radiation: electromagnetic radiation called
gamma rays; fast-moving electrons called beta particles; and alpha particles, which are the nuclei of
helium atoms. If radioactive material is placed at the bottom of a hole in a lead block, radiation will be
emitted through the top. If the beam passes through an electric field, it will separate into the three
types of radiation.
Radioactivity
•
Ranges of alpha. Beta and gamma rays
Radioactivity
Particles: alpha (α), beta (β)
Waves: gamma (γ)
Radioactivity
•
Alpha decay:
226
•
Beta decay:
14
6C
→ 147N + 0-1e
(β = 0-1e)
•
Positron emission:
11
6C
→ 115B + 01e
(anti-electron)
•
Electron capture:
11
6C
+ 0-1e → 115B
•
gamma-ray (high energy photons) emission
88Ra
→ 42He + 22286Rn
Spontaneous emission of particles from
unstable nuclei
(α = 42He)
Radioactive
Decay
Alpha decay:
226
88Ra
→ 42He + 22286Rn
(α = 42He)
Radioactive
Beta decay:
Decay
137
55Cs
→ 13756Ba + 0-1e
Neutron splits:
1 n→ 1 p + 0 e
0
+1
-1
Positron emission:
22
11Na
→ 2210Ne + 01e
Proton splits:
1 p → 1 n + 0 e
+1
0
+1
Radioactive Decay
Gamma decay:
137m
56Ra
→ 13756Ba + γ
Question
Predict the decay products of the alpha emission of 23994Pu
By law of conservation of mass and energy:
239 Pu
94
→ 23592U + 42He
Radioactivity
•
Transmutation of elements
Figure 13.9: Example of radioactive decay: the beginning of decay of 238U.
Radioactivity
Figure 13.10: The half-life of a nucleus is the time it takes for one half of the original amount of that
substance to decay. Radioactive decay is an exponential process.
Radioactivity
Half-life: the time required
for half the radionuclide to
decay
e.g. caesium-137
t1/2 = 30.3 yr
Radioactivity
•
Rate of decay is proportional to amount remaining
dN
dt
•
N , let λ = constant

dN = -λN
dt
Solve for N,
N = Noe-λt
•
•
Where N = no. nuclei at time t, N0 = no. nuclei at start, λ = decay constant
Half-life t1/2 when N = N0
2
Question
N = Noe-λt
Solve for t1/2, N = N0 /2
N0 / 2 = Noe-λt
1/2 = e-λt
Rule of logs
ln(1/2) = ln(2-1) = -ln2 = - λ t1/2
ln ab = b lna
λ = ln 2
t1/2
Question
Derive the expression for the time to decay:
t = t1/2 ln (N / N0)
-0.693
from
N = Noe-λt
Radioactivity
Isotope
Half-life
Nitrogen-16
7 sec
Argon-41
1.8 hours
Radon-222
3.8 days
Iodine-131
8 days
Strontium-90
29 years
Radoium-226
1,599 years
Plutonium-239
24,000 years
Uranium-235
7 x 108 years
Uranium-235
4.5 x 109 years
Most
unstable
Least
unstable
Radioactivity
•
•
t1/2 is related to probability of any one nuclei decaying
Larger the λ, the higher the probability of decay, the shorter the half-life
Radionuclide
λ (s-1)
t1/2
More active,
•
Lead-210
9.86 x 10-10
22.3 yr
Radon-222
2.11 x 10-6
3.8 d
More
disintergrations
With a mix of radioactive waste there is a progression from highly active,
short half-life isotopes to less active, long-lived isotopes
Radioactivity
•
•
Number of atoms that disintergrate per second is called the activity
Measured in Becquerels (Bq):
1 Bq = 1 disintergration per second
•
Quantity of radioactive substance in which 37 x 109 atoms decay per second has activity of 1 curie
(= 1 g Radium)
A=λN
•
•
Where A = activity (Bq), λ = decay constant (= ln2 / t1/2), N = no. radiaoctive atoms present
Short half-lives yield high activities
Radioactivity
•
14C
produced via cosmic rays
1 n
0
+ 147N → 146C + 11H
•
Atmospheric 14C is found in 14CO2
•
Incorporated into plants where it decays
– Whilst alive 14C/12C ratio is constant
– After death 14C no longer replaced from
envionment
– Useful for about 7 half-lives
– Sample must be organic!
t1/2 = 5,730 yr
Question
A fossil is found to have 35 % of the amount of carbon-14 of a currently
living organism. How old is it?
t = t1/2 ln (N / N0)
-0.693
t = 5730 x ln (35/100)
-0.693
t = 8680 yrs
Turin Shroud
Radioactivity
•
For older objects, rocks and minerals other elements are used
– Uses proportions of parent and daughter material
e.g. 238U decays to 206Pb
•
•
Measuring % lead in these rocks allows age determination
4.5 billion year t1/2 of 238U allows very old rocks to be dated
e.g. Earth rocks dated to 3.7 billion years, moon 4.2 billion
End
• Review
Nuclear Physics
Atomic Mass and Energy
•
1 amu = 1/12 mass of C-12 nucleus = 1.66 x 10-27 kg
Energy = mc2
= 1.66 x 10-27 x (3 x 108)2 = 1.5 x 10-10 J
•
1 Electron-volt is the energy gained by e- accelerated in electric field of
1 volt:
E = qV
(Where q = charge on e- = 1.6 x 10-19 C,  1 eV = 1.6 x 10-19 J)
•
Common unit of energy in nucleus is MeV,
1 eV
1.6 x 10-19 J
x 1.5 x 10-10 J = 931 x 106 eV
1 amu
amu
1 amu = 931 MeV
Nuclear Physics
Stability
•
•
Heavy nuclei stable if
N>Z
Plot N vs. Z stable nuclei
Linear up to Z = 20,
N > Z = neutron excess
Why are only some nuclei stable?
N dilute p+ - p+ repulsion and
provide attractive force to
balance electric repulsion of
increasing p+
strong nuclear force
Light nuclei stable if N
=Z
Nuclear Physics
Stability
•
Elements Z > 83 unstable
•
p+ - p+ repulsion cannot be
compensated for by adding N
Heavy nuclei stable if
N>Z
Light nuclei stable if N
=Z
Nuclear Physics
Binding Energy and Mass Defects
•
•
•
•
Mass of a nucleus is always less than the sum of the individual masses of the protons
and neutrons which constitute it
The difference is a measure of the nuclear binding energy
Calculated from the Einstein relationship: E = Δmc2
For the alpha particle Δm= 0.0304 u which gives a binding energy of 28.3 MeV.
Nuclear Physics
Binding Energy and Mass Defects
•
•
He nucleus does not spontaneously split - energy must be added
Law conservation of energy:
Energy of the composite object + energy expended to split it up = sum of the
energies of the separate parts after the split
Energy of the composite object =
sum of the energies of its parts - energy needed to split the object apart
[= binding energy]
matom < mparts
Nuclear Physics
Binding Energy and Mass Defects
•
•
Compare to binding energy of an electron in an atom
The nuclear binding energies are on the order of a million times greater than the
electron binding energies of atoms
Nuclear Physics
Binding Energy and Mass Defects
•
Energy released
– Creates heat in nuclear reactor
– Heats up the earth’s core
– Makes the sun shine
– Used to blow up Hiroshima
High binding energy =
most stable – difficult
to break up
Explains abundance of Fe
Nuclear Physics
Binding Energy and Mass Defects
In this region of nuclear
size, electromagnetic
repulsive forces are
beginning to gain against
the strong nuclear force
Figure 13.11: Just as it takes energy to pull two magnets apart, energy is also necessary to pull
apart the nucleons that are bound together in the nucleus. The total binding energy is the energy
required to disassemble the entire nucleus.
Fig. 13-11, p. 440
Figure 13.12: Rutherford’s apparatus to study nuclear reactions. The protons p produced in
the transmutation of 14N are detected in the scintillator. The incident alpha particles are
produced in the decay of the 210Po.
Fig. 13-12, p. 442
Figure 13.13: Van de Graaff accelerator. Nuclei are accelerated by a high-voltage (9 million
volts) terminal located within each of the cylindrical tanks. The accelerated particles travel
within an evacuated beam tube (shown emerging from the tank). In the foreground is an
electromagnet that deflects the beam of particles into a room to the right, where experiments
are conducted.
Fig. 13-13, p. 443
Two types of detectors for measuring radon concentrations. These devices are exposed to
air in your home for a specified time, then sent to a laboratory for analysis.
Part (a), p. 444
Figure 13.14: A modern form of the Periodic Table of the elements. Elements
that behave the same chemically are in columns.
Fig. 13-14a, p. 449
Figure 13.14: A modern form of the Periodic Table of the elements. Elements that
behave the same chemically are in columns.
Fig. 13-14b, p. 449
End
• Review
Fission
•
Nuclear fission is the splitting of
a large nucleus into smaller
nuclei
•
Energy is released because the
sum of the masses of these
fragments is less than the
original mass
235
1 n → 236 U* →
U
+
92
0
92
90
144 Ba + 21 n
Kr
+
36
56
0
Fission
•
Daughter products mass 75 – 160
235
•
energy
92U
+ 10n → 23692U*
Natural uranium is a mixture of 238/235
isotopes
235U
is a fissile isotope (slow neutrons)
only 0.7% natural uranium
→
90
36Kr
→
90
37Rb
+ 14456Ba + 210n
+ 14355Cs + 310n
Produce
different
# 10n
Fission
235
92U
+ 10n → 23692U* →
148
57La
+ 8535Br + 310n
Uranium-235 = 235.1 Lanthanum-148 = 148.0
Neutron = 1.009
Bromine-85 = 84.9
3 neutrons = 3.027
Total = 236.109
Total = 235.927
Δm = 0.182 = 0.2
Fission
E = mc2
•
Consider this: c2 is equal to 9.0 × 1016 m2 s-2
•
When mass is in kg, the energy units are kg m2 s-2, which is equivalent to 1 joule
•
1 amu = 1/12 mass of C-12 nucleus = 1.66 x 10-27 kg
Energy
•
= mc2
= 1.66 x 10-27 x (3 x 108)2 = 1.5 x 10-10 J
The large value of c2 means that it should be possible to obtain a tremendous amount of energy
from a small amount of matter - whether in a power plant or in a weapon
Question
How much energy is theoretically available in 1 kg uranium-235 (25 x 1023) atoms?
1 amu = 1/12 mass of C-12 nucleus = 1.66 x 10-27 kg
Energy
= mc2
= 1.66 x 10-27 x (3 x 108)2 = 1.5 x 10-10 J
E = 0.182 x 1.5 x10-10 J
E = 7.1 x 1013 J
E = 71 x 106 MJ
x 25 x 1023
Compared with 29 MJ in 1 kg coal
Summary