LECTURE 23
NUCLEI
Instructor: Kazumi Tolich
Lecture 23
2
Reading chapter 32.1 to 32.2
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Nucleus
Radioactivity
Mass and energy
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The famous equation by Einstein tells us that mass is a form of energy.
𝐸 = 𝑚𝑐 %
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In nuclear bomb, nuclear power plants, or the sun, nuclear reactions
cause mass to disappear releasing a huge amount of energy.
disappearance of ~1.6 g of mass is responsible for 9.0 × 10%, MeV
of energy released by the nuclear bomb that destroyed Hiroshima.
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Nucleus
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The atomic number, 𝑍, is the number of protons, the neutron number, 𝑁, is the number of
neutrons, and the mass number, 𝐴, is the number of nucleons of the nucleus.
𝐴=𝑍+𝑁
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The notation for a particular nucleus of element 𝑋 is written as
3
2𝑋
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Two or more nuclei that have the same number of protons but have different number of
neutrons are called isotopes.
The atomic mass unit is defined to be 𝑢 = 1.661 × 106%7 kg = 931.5 MeV⁄𝑐 % , is
defined so that the mass of A%,C is exactly 12𝑢.
Quiz: 1
5
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There are 82 protons in a lead nucleus. Why doesn’t the lead nucleus
burst apart due to their mutual repulsion?
A.
B.
C.
D.
E.
F.
Coulomb repulsive force doesn’t act inside the nucleus.
Gravity overpowers the Coulomb repulsive force inside the nucleus.
The negatively charged neutrons balance the positively charged protons.
The negatively charged electrons balance the positively charged protons.
Protons lose their positive charge inside the nucleus.
None of the above
Quiz: 23-1 answer
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None of the above
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Strong nuclear force binds them together.
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Its range is observed to be about 10-15 m or fermi.
It is attractive and acts with nearly equal strength between protons
and protons, protons and neutrons, and neutrons and neutrons.
Most nuclei are spherical with radii approximated by
𝑟 = 1.2 × 106AD m 𝐴A⁄F
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By contrast, the radius of an atom is on the order of 10-10 m.
This means that the density of the nucleus is extremely high.
Quiz: 2
7
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Which of the following is/are correct regarding the stability of nuclei?
Choose all that apply.
A.
B.
C.
D.
E.
F.
For light nuclei, the greatest stability is achieved when 𝑁 ≈ 𝑍.
For light nuclei, the greatest stability is achieved when 𝑁 > 𝑍.
For light nuclei, the greatest stability is achieved when 𝑁 < 𝑍.
For heavy nuclei, the greatest stability is achieved when 𝑁 ≈ 𝑍.
For heavy nuclei, the greatest stability is achieved when 𝑁 > 𝑍.
For heavy nuclei, the greatest stability is achieved when 𝑁 < 𝑍.
Quiz: 23-2 answer
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For light nuclei, the greatest stability is achieved when
𝑁 ≈ 𝑍.
For heavy nuclei, the greatest stability is achieved
when 𝑁 > 𝑍.
For heavier nuclei such as %FL
K%U, instability caused by
the electrostatic repulsion between the protons is
minimized when there are more neutrons than protons.
Every isotope with 𝐴 ≥ 84 is radioactive.
There are many radioactive isotopes of lighter
elements as well such as AP,C and FAH.
Three types of radiation
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1.
A unstable nucleus can decay into a stable nucleus. Any of
three different types of particles may be emitted:
Alpha particles, which consist of two neutrons and two
protons, and are nuclei of P%He.
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2.
Electrons (or positrons), also called beta rays. Positrons is
an antiparticle of electron and have the same mass as
electrons but are positively charged.
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3.
𝛼 rays can barely penetrate a sheet of paper.
𝛽 rays (both
aluminum.
𝛽6
and
𝛽T)
can penetrate a few millimeters of
Gamma rays are high-energy photons.
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𝛾 rays can penetrate several centimeters of lead.
3
2
Quiz: 3
10
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A uranium nucleus %FL
K%U undergoes an alpha decay. What is/are its
decay product(s)?
A.
B.
C.
D.
E.
F.
%FL
P
K%U + %He
%FP
P
KVU + %He
%FP
P
KVTh + %He
P
%He
%P%
P
KPPu + %He
%F,
P
LLTh + %He
Quiz: 23-3 answer
11
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%FP
KVTh
+ P%He
When a nucleus decays by emitting an alpha
particle, it loses two protons and two neutrons:
P
3
36P
2𝑋 → 26%Y + %He.
Here, 𝑋 is the parent nucleus and 𝑌 is the
daughter nucleus.
%FL
%FP
P
U
→
Th
+
%He
KV
K%
Quiz: 4
12
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A uranium nucleus %FL
K%U (initially at rest) decays into a thorium nucleus
%FP
KVTh and an alpha particle. Which one has the greater momentum?
A.
B.
C.
%FP
KVTh
nucleus
alpha particle
The magnitudes of the momenta for both particles are the same.
Quiz: 23-4 answer
13
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The magnitudes of the momenta for both particles are the same.
By momentum conservation, they must have the same magnitude of
momentum since the initial momentum was zero.
This follows that the decay products are emitted in the opposite
directions.
Quiz: 5
14
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What is the daughter nucleus when a potassium nucleus
undergoes a 𝛽 6 -decay?
A.
B.
C.
D.
E.
F.
PV
%VCa
PV
%VK
F,
A7Cl
FP
%ASc
PV
ALAr
PV
ALK
PV
AKK
Quiz: 23-5 answer
15
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PV
%VCa
In a 𝛽6 -decay, a neutron is converted into a proton,
an electron and an antineutrino: AVn → AAp + e6 + 𝜈̅i
The charge is conserved.
A nucleus that undergoes a 𝛽6 -decay loses a neutron
and gains a proton: 32𝑋 → 2TA3𝑌 + e6 + 𝜈̅i
PV
AKK
6
→ PV
%VCa + e + 𝜈̅i
If a nucleus undergoes a 𝛽T -decay, a proton has
become a neutron emitting a positron and a neutrino, :
3
3
T
2𝑋 → 26A𝑌 + e + 𝜈i
Quiz: 6
16
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Suppose that the radii of two nuclei X and Y are about the same. X
undergoes an alpha decay, and Y undergoes a beta decay. How do
the radii of the daughters of X and Y compare?
A.
B.
C.
The radius of X’s daughter is smaller than that of Y’s daughter.
The radius of X’s daughter is larger than that of Y’s daughter.
The radius of X’s daughter is about the same as that of Y’s daughter.
Quiz: 23-6 answer
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The radius of X’s daughter is smaller than that of Y’s daughter.
The radius of a nucleus is approximated by 𝑟 = 1.2 × 106AD m 𝐴A⁄F .
The radius of X’s daughter is smaller than that of X because the atomic
P
number 𝐴 went down by 4: 32𝑋 → 36P
26%𝑌 + %He
But the radius of Y’s daughter is same as that of Y because the atomic
number 𝐴 remains the same: 32𝑋 → 2TA3𝑌 + e6 + 𝜈̅i
Beta decay and discovery of neutrinos
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During a 𝛽6 -decay, a parent nucleus 32𝑋 decays into a daughter nucleus 2TA
𝑌 by
emitting an electron.
If this were a two body decay ( 2TA3𝑌 and e6 ), the kinetic energy of e6 can only be one
value (from conservations of energy and momentum).
But experiments showed that the kinetic energy of e6 is a continuous spectrum.
This lead to a discovery of another particle emitted in the decay, called “neutrinos.”
Quiz: 7
19
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An excited nucleus undergoes a gamma decay. How do the atomic
number and neutron number change?
A.
B.
C.
D.
E.
The atomic number increases by 1, and the neutron number remains the
same.
The atomic number remains the same, and the neutron increases by 1.
The atomic number decreases by 1, and the neutron number remains the
same.
The atomic number remains the same, and the neutron decreases by 1.
The atomic and neutrons numbers both remain the same.
Quiz: 23-7
20
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The atomic and neutrons numbers both remain the same.
Alpha and beta decays are often followed by a gamma decay.
A gamma ray is a photon emitted by a nucleus as it returns to its
ground state.
Demo: 1
21
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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)
Radioactive decay series
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Heavy nuclei decaying via alpha
emission may very well decay to a
daughter nucleus which is also unstable.
The decays will continue until a stable
nucleus is reached.
An original parent nucleus producing a
series of decays is called a radioactive
decay series.
Activity
23
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Some nuclei decay more rapidly than others.
The time rate of decay is called the activity.
The units of activity are either curie (Ci) or becquerel (Bq).
= 3.7 × 10AV decays⁄s
¤ 1 Bq = 1 decay⁄s
¤ 1 Ci