physics 1201 final exam information – spring 2013
TRANSCRIPT
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Physics 1201 Final Exam information – Spring 2013
1) Format: 35 multiple-choice questions, 5 points each à 175 points total
2) Closed book and closed notes
3) Equations and constants are provided on the final exam
4) Cumulative – it covers all of the material covered in the course
5) Approximate weightings of material: ~10 questions from material covered for midterm 1 ~10 questions from material covered for midterm 2 ~15 questions on material covered since midterm 2 6) See the Assignment Sheet for the date and time of your final exam
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PRELIMINARY
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PRELIMINARY
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Chapter 30
Nuclear Physics and Radioactivity
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Radioactivity
A magnetic field separates three types of particles emitted by radioactive nuclei. The decay takes the general form:
parent→ daughter + x
Q ≡mparentc2 − mdaughter +mx( )c2 ⇒Q− value→ KE released
Q > 0⇒ exothermic Q < 0⇒ endothermic
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Radioactivity α DECAY
ZAP → Z−2
A−4 D + 24 He
Q =mPc2 − mD +mα( )c2
= 238.0508 u− 234.0436 u+ 4.0026 u( )"# $% 931.5MeVu
&
'(
)
*+
= 4.3MeV
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Radioactivity
A smoke detector
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Radioactivity
β DECAY
e D P 011 −+ +→ A
ZAZ
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Radioactivity
γ DECAY
γ P P +→∗ AZ
AZ
excited energy state lower energy
state
88226Ra*→ 88
226Ra+γ Eγ = 0.186 MeV
a photon that originates from the energy-level transition of the nucleus
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The Neutrino
During beta decay, energy is released. However, it is found that most beta particles do not have enough kinetic energy to account for all of the energy released. The additional energy is carried away by a neutrino à
90234 Th → 91
234 Pa + −10 e + ν
mass ≈ 0, q = 0
A free neutron beta decays in about 12 minutes,
01n → 1
1p + −10 e + ν
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Radioactive Decay and Activity
The half-life of a radioactive decay is the time in which ½ of the radioactive nuclei disintegrate.
with calculus⇒ N = Noe−λ t
λ2ln
21 =T
ΔN = −λNΔt, λ = decay rate s−1( )∴ΔNΔt
= −λN ⇒ #decayed / time⇒ activity
The number of nuclei decaying, ΔN, in a time Δt in a population of N nuclei is given by,
initial population
SI for activity = becquerel = Bq = 1 decay/s 1 Curie = 1 Ci = 3.70 x 1010 Bq
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Radioactive Decay and Activity
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Example: Activity per gram of in a living organism. a) Determine the number of atoms present for every gram of in a living organism. b) Find the decay constant and c) the activity of this sample. Assume that in a living organism there is one atom of for every 8.3 x 1011 atoms of
614C614C
612C
614C
612C
a) #atoms 614C
1 gram 612C
=112mol
!
"#
$
%& 6.02×1023
atomsmol
!
"#
$
%&
18.3×1011!
"#
$
%&= 6.0×1010atoms
b)T1 2 = 5730 yr =1.81×1011s
λ =0.693T1 2
=0.693
1.81×1011s= 3.83×10−12 s−1
c) ΔNΔt
= λN = 3.83×10−12 s−1( ) 6.0×1010atoms( ) = 0.23 Bq
When an organism dies, this activity begins to decay away.
Activity of for every gram of in a living organism
614C
612C
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Radioactive Dating dating of the “Ice Man.” 6
14C
The “Ice Man” was found in the Italian Alps in 1991. If the body has a activity of 0.121 Bq per gram of carbon, find the age of the Ice Man’s remains.
614C
NN0
= e−λt ⇒ ln NN0
#
$%
&
'(= −λt
t = − 1λ
#
$%
&
'(ln
NN0
#
$%
&
'(
activity ≡ A = ΔNΔt
= λN ⇒NN0
=λNλN0
=AA0
∴t = − 1λ
&
'(
)
*+ln
NN0
&
'(
)
*+= −
T1 20.693&
'(
)
*+ln
AA0
&
'(
)
*+= −
5730 yr0.693
&
'(
)
*+ln
0.1210.23
&
'(
)
*+
= 5300 yr
Know λ Need to find
NN0
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Radioactive Decay Series
The sequential decay of one nucleus after another is called a radioactive decay series.
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Radioactive Decay Series
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Chapter 31
Nuclear Energy, Effects and uses
of radiation
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Induced Nuclear Reactions
A nuclear reaction is said to occur whenever the incident nucleus, particle, or photon causes a change to occur in the target nucleus.
Charge and nucleon number are conserved in a nuclear reaction.
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Induced Nuclear Reactions
Example: An Induced Nuclear Transmutation An alpha particle strikes an aluminum nucleus. As a result, and unknown nucleus and a neutron are produced.
P3015
24He + 13
27Al→ ZAX + 0
1n
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Induced Nuclear Reactions
Nuclear reactions can produce elements not found in nature……. ……an induced nuclear reaction in which uranium is transmuted into the transuranium elements neptunium and finally plutonium.
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Nuclear Fission
A slowly moving neutron causes the uranium nucleus to fission into barium, krypton, and three neutrons.
Average energy released in the fission reaction
n+ 92235U⇒≈ 200 MeV
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Nuclear Fission
A chain reaction
….assuming each fission creates two neutrons which can cause addition fissions in other nearby nuclei….. This results in an uncontrolled chain reaction à e.g. atom bomb
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Nuclear Fission
In a controlled chain reaction, only one neutron, on average, causes another neutron to fission. This is the reaction mode used in nuclear reactors.
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Nuclear Reactors
A nuclear reactor consists of fuel elements, control rods, and a moderator.
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Nuclear Reactors
The moderator slows neutrons and the control rods absorb neutrons.
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Nuclear Fusion
Two nuclei of very low mass can combine to generate energy. This process is called nuclear fusion.
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Nuclear Fusion
12H + 1
3H→ 24He+ 0
1n
energy released = Δm( )c2
= m 12H( )+m 1
3H( )−m 24He( )−m 0
1n( )$%
&'c
2
= 2.0141u+3.0161u− 4.0026 u−1.0087 u[ ] 931.5 MeVu
(
)*
+
,-
= 0.0189 u[ ] 931.5 MeVu
(
)*
+
,-=17.6 MeV