Download Radioactivity

Radioactivity
Types of particles:
Alpha particles
• Two protons + two
neutrons
• Same as helium-4
nucleus
• + 2 charge; deflected
by a magnetic field,
and attracted to
negative charges
Alpha particles
• Largest particle of
radioactivity
• Short range
• Stopped by sheet of
paper
• Most damaging due
to large mass
Alpha tracks in a cloud
chamber
Nuclear equations
• Mass must be conserved
• Mass numbers and atomic numbers must have same
sum on each side of equation
• Result of alpha emission: mass number decreases by 4,
atomic number decreases by 2
• Note symbol for alpha particle – sometimes written 42a or
just a
Beta Particles
• Consist of free
electrons
• Low mass, -1 charge
• Medium range,
medium penetrating
power
• Stopped by thick
wood, thin sheet of
lead
b
• Symbol is the Greek
letter beta or 0-1e
• Produced by a
neutron, which turns
into a proton
Nuclear equations
• In beta decay a neutron turns into a proton and
ejects an electron
• Mass number does not change, and atomic
number increases by 1
• Example of transmutation
Gamma Radiation
• Consists of highenergy photons
• No rest mass, no
charge
• Not deflected by
magnetic field
• Long range, very
penetrating
• Accompanies many
other types of decay
g
• Symbol is Greek letter
gamma
• Only product of IT –
internal transition
• Produces no change
of mass or atomic
numbers
Other types of decay
Positron Emission
• Positrons are the
electron’s antiparticle
• Same characteristics
as electron, except for
positive charge
• Symbol: b+ or 01e
Positron Emission Tomography
(PET scan)
Positron emission
• In positron emission a proton ejects a positron
and becomes a neutron
• Mass number does not change
• Atomic number decreases by one
Electron Capture
• If there are too many
protons in a nucleus,
it may capture an
electron
• A proton becomes a
neutron
Symbol for an electron
Electron capture
• Mass number stays the same
• Atomic number decreases by one
• Same result as positron emission
Nuclear Stability
• Nuclear particles (protons and neutrons)
are called nucleons
• Nucleons are held together by nuclear
strong force (short range, very strong)
• Neutrons are “glue” – necessary to hold
the nucleus together
• Without neutrons the nucleus would fly
apart due to electrostatic repulsion
Nuclear Band of Stability
Nuclear Magic Numbers
• Nuclei with certain numbers of protons or
neutrons are especially stable
• “Magic numbers” are 2, 8, 20, 28, 50, 82,
and 126
• When both neutrons and protons are
magic numbers, the nucleus is specially
stable: 20882Pb
Nuclear Magic Numbers
• Most stable nuclei have the same “magic
number” of protons and neutrons: 42He,
16 O, and 40 Ca
8
20
• “Even-odd” rule: Nuclei with even
numbers of protons and neutrons are
more stable than odds:
• Stable isotopes: 264
• Both even: 157 Both odd: 5
Stability and Decay
• Above the stability band: Too many
neutrons
• Beta decay reduces the neutron/proton
ratio
• Very large nuclei (Z>83) undergo alpha
decay, which reduces the size of the
nucleus
Stability and decay
• Below the band of stability: too many
protons
• Positron emission or electron capture
• Protons are reduced, neutrons increased
1 p
1 n + 0 b
1
0
1
1
1p +
0
-1e
1
0n
Decay series
Induced Transmutation
• Transmutation can be induced by allowing
high-energy particles to strike atomic
nuclei
4 He + 14 N  17 O + 1 p
2
7
8
1
238 U + 1 n  239 U  239 Np + 0 e
92
0
92
93
-1
239 Np  239 Pu + 0 e
93
94
-1
1 n
0
+ 147N  146C + 11H
Radioactive Decay
decay
Radioactive
• Radioactive isotopes decay at
predictable rates
• Half Life: the time it takes for 1/2 of a
sample to decay
• Half of the remaining sample decays
every half life period
Half Life Graph
Half Life
• Follows exponential decay
• Moment of decay of any one particle is
unpredictable
• Example: Radon-222 decays with a half
life of 3.8 days. Approximately how long
will it take for 9.5 grams of a 10 gram
sample to decay?
Half Life Problems
• Solution: Divide sample mass in half until
0.5 grams or less is reached.
10/2 = 5 (one half life)
5/2 = 2.5 (two half lives)
2.5/2 = 1.25 (three half lives)
1.25/2 = 0.625 (four half lives)
0.625/2 = 0.3125 (five half lives)
Half life Problems
• Four half lives = 4 HL x 3.8 days/HL = 15.2
days
• Five half lives = 5 HL x 3.8 days/HL = 19
days
• Therefore, 9.5 grams of a 10 gram sample
will decay in somewhere between 15.2
and 19 days.
Half Life Problems
• Example #2: Sally has a 15.0 g sample of
phosphorus-32 (half life 14.28 days).
About how much will be left two months
later (60 days)?
• Find time in half-lives: 60 days/14.28
days/HL = 4.20 half lives.
• Multiply the sample mass by (1/2)y, where
y = number of half-lives (use xy key on
calculator)
Half Life Problems
• 15.0g(1/2)4.20 = 15.0g(0.0544) = 0.816 g
remaining
• Half life equation: Nt = N0(1/2)t/t1/2 or
Nt = N0e-lt where l is the decay constant
t = (t1/2/0.693)ln(N0/Nt)
Nuclear Reactions and Energy
• Mass is not strictly conserved in nuclear
reactions
• Some mass is lost as energy
Nuclear Reactions and Energy
• Mass to energy conversion is governed by
DE = Dmc2, where c = the speed of light in
a vacuum (3.0x108m/s)
• Nuclear binding energy is the energy lost
when the nucleus is formed.
• Mass equivalent of the nuclear binding
energy is the mass defect.
• Protons and neutrons in the nucleus have
less mass than separate nucleons
Calculating Binding Energy
•
•
•
•
•
Example:
Mass of 1 proton = 1.00735 amu
Mass of 1 neutron = 1.00875 amu
Mass of 1 electron = 0.0005485 amu
If 1 amu = 1.66 x 10-24g, calculate the
binding energy of an atom of helium-4
(mass 4.00260325415 amu)
Binding energy of helium-4
• Mass of constituents
Protons: 1.00735 amu/p(2p) = 2.01470 amu
Neutrons: 1.00875 amu/n(2n) = 2.01750 amu
Electrons: 0.0005485 amu/e(2e) = 0.001097
amu
Total: 4.03330 amu
4.03330 amu(1.66x10-24g/amu) = 6.70x10-24g
Helium atom: 4.0026amu(1.66x10-24g/amu) =
6.64x10-24g)
Binding energy of helium-4
• Mass deficit = 6.70x10-24g - 6.64x10-24g =
0.06x10-24g = 6x10-26g = 6x10-29kg
• Binding energy: DE = Dmc2
• DE = 6x10-29kg(3.00x108m/s)2 = 5x10-12J
• Energy per gram: one gram of helium-4
would have 1g/(6.64x10-24) = 1.51x1023
atoms
• 1.51x1023 a/g(5 x 10-12J/a) = 8 x 1011J/g
Binding energy of helium-4
•
•
•
•
8 x 1011J/g(1 kW-hr/3600 J) = 2 x 108 kW-hr
Average household uses 10,656 kW-hr/yr
2 x 108 kW-hr/10,656 kW-hr/(house-yr) = 20,000
Binding energy in one gram of helium-4 could
power 20,000 average households for one year
• Alternatively, it could power one house for
20,000 years, or Al Gore’s mansion for 904
years.
Nuclear Fission
• Some larger nuclei will split into two parts
when struck by a neutron
• The two smaller nuclei are more stable, so
energy is released
• The two smaller nuclei will have a higher
binding energy per nucleon
• Neutrons are also released, producing a
chain reaction
Nuclear Fission
Nuclear chain reactions
• Occur if the product of the reaction is
necessary to start new reactions
1
0n
+ 23592U --> 23692U --> 9236Kr + 14156Ba + 310n
• Critical mass - minimum mass necessary
to sustain a chain reaction
• Large enough critical mass will explode
Nuclear Power Plants
• Nuclear fuel is usually
a supercritical mass
of U-235 enriched
uranium
• Reaction is promoted
by a moderator - a
material that slows
neutrons down so
they will cause fission
- usually carbon or
D2O
Nuclear reactor at Chernobyl
Nuclear Power Plants
• Reaction is controlled
by control rods
(cadmium or boron),
which absorb
neutrons
• Reaction generates
heat, which makes
steam to run a turbine
CROCUS, a small research
nuclear reactor
Geiger Counter
• Counts individual
particles of radioactivity
• Ionizing radiation enters
the tube through a mica
window
• Ionization of gas in tube
allows current to flow for
an instant between high
voltage cathode and
anode