Nuclear Binding, Radioactivity
Physics 102: Lecture 27
• Make sure your grade book entries are correct!
e.g. HOUR EXAMS, “EX” vs. “AB”
EX = excused, AB = absent = 0 credit
• Honors projects are due May 3
via email: Word/PDF, file name to include your full name
• Please fill out on-line ICES forms
More important announcements
• No discussion next week! (Disc. 13)
• Lecture Wed. (May 5) will cover material– Bring “Physics 102 problem solver”– Come prepared!– Quiz (put in TA mailbox by Friday, May 7)
• FINAL EXAM May 10 & 11– Review session Sunday May 9, 3pm, 141
Loomis
Hydrogen atom: Binding energy =13.6eV
Binding energy of deuteron = or 2.2Mev! That’s around 200,000 times bigger!
2.2106eV
Simplest Nucleus: Deuteron=neutron+proton
neutron proton
Very strong force
Coulomb force
electron
proton
Strong Nuclear Force
(of electron to nucleus)
ground state
2.2 MeV
Deuterium Binding Energy
Nuclei have energy level—just like atoms
12C energy levels
Note the energy scale is MeV rather than eV
energy needed to remove a proton from 12C is 16.0 MeV
energy needed to remove a neutron from 12C is 18.7 MeV
Comparing Nuclear and Atomic sizes
Hydrogen Atom: Bohr radius = 5.2910 11m
Nucleus with nucl number A: r A1/3 (1.210 15m)
Note the TREMENDOUS difference
Smaller is Bigger!
Nucleus is 104 times smaller and binding energy is 105 times larger!
13
1327Al has radius r 3.61015m
A
Z
Preflight 27.2
Where does the energy released in the nuclear reactions of the sun come from?
(1)covalent bonds between atoms 17%
(2)binding energy of electrons to the nucleus 36%
(3)binding energy of nucleons 47%
15
Binding Energy
Einstein’s famous equation E = m c2
Proton: mc2 = 938.3MeVNeutron: mc2= 939.5MeV
Deuteron: mc2 =1875.6MeV
Adding these, get 1877.8MeV
Difference is Binding energy, 2.2MeV
MDeuteron = MProton + MNeutron – |Binding Energy|
17
proton:mc2=(1.67x10-27kg)(3x108 m/s)2=1.50x10-10 J
ACT: Binding Energy
Which system “weighs” more?
1) Two balls attached by a relaxed spring.
2) Two balls attached by a stretched spring.
3) They have the same weight.
M1 = Mballs + Mspring
M2 = Mballs + Mspring + Espring/c2
M2 – M1 = Espring/c2~ 10-16 Kg
19
Iron (Fe) has most binding energy/nucleon. Lighter have too few nucleons, heavier have too many.
BIN
DIN
G E
NE
RG
Y in
MeV
/nu
cleon
92238U
10
Binding Energy Plot
Fission
Fusi
on Fusion = Combining small atoms into large
Fission = Breaking large atoms into small
21
Which element has the highest binding energy/nucleon?
Preflight 27.3
22
• Neon (Z=10) 31%
• Iron (Z=26) 22%
• Iodine (Z=53) 47%
Which of the following is most correct for the total binding energy of an Iron atom (Z=26)?
9 MeV
234 MeV
270 MeV
504 Mev
For Fe, B.E./nucleon 9MeV
2656Fe has 56 nucleons
Total B.E 56x9=504 MeV
Preflight 27.4
24
13%
28%
31%
28%
particles: nuclei 24He
particles: electrons
: photons (more energetic than x-rays) penetrate!
3 Types of Radioactivity
Easily Stopped
Stopped by metal
26
Radioactive sources
B field into screen
detector
92238U 90
234Th: example
24He recall
: example
Decay Rules
1) Nucleon Number is conserved.2) Atomic Number (charge) is conserved.3) Energy and momentum are conserved.
: example 00
* PP AZ
AZ
1) 238 = 234 + 4 Nucleon number conserved
2) 92 = 90 + 2 Charge conserved
e0111
10 pn
Needed to conserve momentum.
30
00
A nucleus undergoes decay. Which of the following is FALSE?
1. Nucleon number decreases by 4 26%
2. Neutron number decreases by 2 45%
3. Charge on nucleus increases by 2 29%
Preflight 27.6
32
decay is the emission of 24He
He42
23490
23892 ThU Ex.
Z decreases by 2(charge decreases!)
A decreases by 4
The nucleus undergoes decay. 90234Th
Which of the following is true?
1. The number of protons in the daughter nucleus increases by one.
2. The number of neutrons in the daughter nucleus increases by one.
decay is accompanied by the emission of an electron: creation of a charge -e.
In fact, inside the nucleus, and the electron and neutrino “escape.”
n p e e
Preflight 27.7
00
01
?????
23490 XTh
e 00
01
23491
23490 PaTh
e
34
ACT: Decay
Which of the following decays is NOT allowed?
HePbPo 42
21082
21484
92238U 90
234Th
40 40 0 019 20 1 0K P e
NC 147
146
1
2
3
4
238 = 234 + 4
92 = 90 + 2
214 = 210 + 4
84 = 82 + 2
14 = 14+0
6 <> 7+0
40 = 40+0+019 = 20-1+0
36
Nt
N
If the number of radioactive nuclei present is cut in half, how does the activity change?
1 It remains the same 24%
2 It is cut in half 50%
3 It doubles 26%
No. of nuclei present
decay constant
Decays per second, or “activity”
Preflight 27.8
38
ACT: Radioactivity
Nt
N
No. of nuclei present
decay constant
Decays per second, or “activity”
Start with 16 14C atoms.
After 6000 years, there are only 8 left.
How many will be left after another 6000 years?
1) 0 2) 4 3) 8Every 6000 years ½ of atoms decay
40
time
N(t)N0e t N0 2
t
T1/2
40
Decay Function
Instead of base e we can use base 2:
N(t)N0e tSurvival:
No. of nuclei present at time t
No. we started with at t=0
e t 2
tT1/2
T1/2
0.693
where
Then we can write N(t)N0e t N0 2
t
T1/2
Half life
Radioactivity Quantitatively
Nt
N
No. of nuclei present
decay constant
Decays per second, or “activity”
42
You are radioactive!
One in 8.3x1011 carbon atoms is 14C which decays with a ½ life of 5730 years. Determine # of decays/s per gram of Carbon.
Nt
N
11
2314 103.8
11002.6
mole12
0.1g
N
2/1
693.T
1-12s1083.36060243655730
693.
gatoms
106 10
decays/s 23.045
Carbon Dating
We just determined that living organisms should have a decay rate of about 0.23 events/s per gram of carbon.
The bones of an ice man are found to have a decay rate of 0.23/2 events/s per gram. We can estimate he died about 6000 years ago.
47
ACT/Preflight 27.9
The half-life for beta-decay of 14C is ~6,000 years. You test a fossil and find that only 25% of its 14C is un-decayed. How old is the fossil?
1. 3,000 years
2. 6,000 years
3. 12,000 years
At 0 years: 100% remains
At 6,000 years: 50% remains
At 12,000 years: 25% remains
49
Summary• Nuclear Reactions
– Nucleon number conserved– Charge conserved– Energy/Momentum conserved– particles = nucleii– - particles = electrons– particles = high-energy photons
• Decays– Half-Life is time for ½ of atoms to decay
50
N(t)N0e tSurvival:
T1/2
0.693
24He
See you next time!
• Take a look at Special Relativity in 14 Easy (Hyper)lessons:
http://web.hep.uiuc.edu/home/g-gollin/relativity/