LECTURE 25
NUCLEI
Instructor: Kazumi Tolich
Lecture 25
2
Reading chapter 40-1 to 40-2
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Nucleus
Radioactivity
Dating with radioactivity
Nucleus
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Protons and neutrons (nucleons) make up a nucleus.
The number of protons, Z, is called atomic number of the
nucleus.
The number of nucleons, A, is called mass number of the
nucleus.
Two or more nuclei that have the same number of protons
but have different number of neutrons are called
isotopes.
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Example: H, 2H, 3H
A=Z +N
Strong force and size of nuclei
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Protons and neutrons are confined in a very small
volume despite the electrical repulsion among protons.
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Strong nuclear force bines them together.
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Its range is observed to be about 10-15 m.
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Most nuclei are spherical with radii approximated by
R ≈ R0 A1 3 ≈ 1.2 fm A1 3
N and Z
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For light nuclei, the greatest stability is achieved when N ≈ Z.
For heavier nuclei, instability caused by the electrostatic
repulsion between the protons is minimized when there are
more neutrons than protons.
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O: Z = 8, N = 8
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238
92
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U: Z = 92, N = 146
Every isotope with A > 84 is radioactive.
There are many radioactive isotopes of lighter elements as
well.
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Examples: 14C and tritium (3H).
Mass and binding energy
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Mass of a nucleus is less than the sum of the masses of its parts by
Eb/c2.
Eb is called the binding energy.
(
)
Eb = ZM H + Nmn − M A c 2
is the mass of the 1H atom (proton).
¤ mn is the mass of the neutron.
¤ MA is the mass of the nucleus.
¤ MH
Discovery of radioactivity
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Radioactivity was first discovered when Becquerel stored unexposed
film next to uranium.
Something exposed the film; Becquerel was able to demonstrate that
this property of the uranium did not change through various chemical
interactions.
Two years later, radium was discovered. It was also radioactive, but
much stronger than uranium.
Three types of radiation
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Radioactive nuclei emit three types of radiation
¤ alpha
rays
¤ beta rays
¤ gamma rays
Alpha decays
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In alpha decay, a radioactive nucleus spits out an alpha
particle, two protons plus two neutrons (identical to a 4He
nucleus).
Alpha decay occurs in nuclei that are too large for the strong
nuclear force to hold them together indefinitely.
The nucleus is more stable if it is smaller, and therefore emits
an alpha particle.
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Eg:
232
Th → 228 Ra + α = 228 Ra + 4 He
Beta decays
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In beta decay, a nucleus emits an electron and an electron anti-neutrino.
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Note that there are no electrons inside the nucleus.
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This electron is called a beta particle.
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The weak nuclear force causes a neutron in the nucleus to spontaneously transform into a proton, an
electron, and an electron-antineutrino.
n → p + e− + ν e
The electron has too much energy to be bound by a proton in the nucleus.
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eg:
14
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C → 147 N + e− + ν e
Beta decay and discovery of neutrinos
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During a beta decay, a parent nucleus (A, Z) decays into a daughter nucleus (A, Z+1) by
emitting an electron.
If this were a two body decay (daughter and e-), the kinetic energy of e- can only be
one value (from conservations of energy and momentum).
But experiments showed that the kinetic energy of e- is a continuous spectrum.
This lead to a discovery of another particle emitted in the decay, called “neutrinos.”
Quiz: 1
12
Gamma decays
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Alpha and beta decays are often followed by a gamma decay.
If a gamma decay does not follow an alpha or beta decay in a short
time, the nucleus is in a metastable state.
A gamma ray is a photon emitted by a nucleus as it returns to its ground
state (the state with the lowest energy).
A and Z stay the same.
Demo 1
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Cloud Chamber
¤ Tracks
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of alpha particles.
Geiger counter
¤ Comparison
n 𝛾 ¤ Salt
between 𝛽 decays and 𝛾 decays.
rays are more penetrating.
substitute is radioactive! (and so are many others, like a banana)
Smoke detectors
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Some smoke detectors uses alpha decays of
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A small amount of
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The alpha particles emitted ionizes the air, allowing a measurable current to flow between the plates.
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241Am
241Am.
is placed between two metal plates connected to an emf source.
When smoke enters the detector, the ionized air molecules stick to the smoke particles and become
neutralized.
This reduces the amount of current flowing between the plates, and sets off the alarm.
Positron Emission Tomography (PET) scanner
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Glucose that contains radioactive tracer (positron emitter) is injected into the
bloodstream.
The glucose is delivered to the part of the brain that is activated.
The positrons from the radioactive tracer annihilate with electrons in the brain,
emitting gamma rays that penetrate through the patient’s skull.
PET scanner monitors the gamma rays.
Nuclear decay functions
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If we started out with N0 nuclei, the number of nuclei remaining at some later time is
N = N 0 e− λ t
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λ is called the decay constant.
The number of decays per unit time is called the decay rate, R, or the activity,
measured in Bq
R = λ N 0 e− λ t = R0 e− λ t
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where R0 = λ N 0 is the decay rate at t = 0.
The average or mean lifetime τ is
τ=
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1
λ
The half-life, t1/2, is defined as the time it takes for N and R to decrease by half.
t1 2 =
ln 2
= τ ln 2 = 0.693τ
λ
Quiz: 2
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Example 1
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A sample of a radioactive isotope is found
to have an activity of 115.0 Bq
immediately after it is pulled from the
reactor that formed the isotope. Its activity
2 h 15 min later is measured to be
85.2 Bq.
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a)
b)
Calculate the decay constant and the halflife of the sample.
How many radioactive nuclei were there in
the sample initially?
Radioactive dating
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If you know how much of a radioactive material has decayed, you can read the elapsed time
from the decay curve.
The half-lives of various nuclei can vary widely.
Carbon dating
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C 𝛽 -decays with a half-life of 5730 years.
Carbon dating uses 14C produced in the upper atmosphere during nuclear reactions
caused by cosmic rays.
14C reacts just like 12C chemically, and the ratio of 14C to 12C in a living organism is
the same as the equilibrium ratio in the atmosphere.
After an organism dies, it no longer absorbs C, so the ratio of 14C to 12C continually
decreases since 14C decays.
The decay rate per amount of C in a sample therefore yields the age of the
previously living organism.
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Quiz: 3
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Refining radioactive dating
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There are also many nonradioactive methods
of dating materials, such as tree ring analysis.
The radioactive and nonradioactive methods
may be used to check each other and refine
the procedure, increasing accuracy of dating.
The 14C method gives lifetimes that are too
short after about 10,000 years, probably due
to fluctuations in the 14C to 12C ratio.
Age of Earth
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The age of Earth is measured to be around 4.54 billion years using radioactivity of
rocks and meteorites.
The type of the rocks used is known to reject lead during its formation.
The method uses two series of α and β decays:
¤ 238U
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(t1/2 = 4.47 billion years ) to 206Pb.
235U (t
207Pb.
1/2 = 704 million years ) to
The age of Earth is determined from the Pb to U ratios.