overview. nucleus = protons+ neutrons nucleons a = nucleon number (atomic mass number) gives you...
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Overview
Nucleus = Protons+ Neutrons
nucleons
A = nucleon number (atomic mass number)
Gives you mass density of element
Z = proton number (atomic number) Gives chemical properties (and name)
N = neutron number
A=N+Z
Recall: Nuclear Physics
Li63
A
Z
Periodic_Table
A material is known to be an isotope of lead
Based on this information which of the following can you specify?
1) The atomic mass number
2) The neutron number
3) The number of protons
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(Isotope of H)
neutron proton
Very strong force
Coulomb force
electronproton
Strong Nuclear Force
(of electron to nucleus)
Can get 4 nucleons into n=1 state. Energy will favor N=Z
Pauli Principle - neutrons and protons have spin like electron, and thus ms= 1/2.
n n p p
n n p p
But protons repel one another (Coulomb Force) and when Z is large it becomes harder to put more protons into a nucleus without adding even more neutrons to provide more of the Strong Force. For this reason, in heavier nuclei N>Z.
# protons = # neutrons
7
ground state
2.2 MeV
Deuteron 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
Where does the energy released in the nuclear reactions of the sun come from?
(1)covalent bonds between atoms
(2)binding energy of electrons to the nucleus
(3)binding energy of nucleons
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|
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.
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
• Neon (Z=10)
• Iron (Z=26)
• Iodine (Z=53)
Which element has the highest binding energy/nucleon?
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
particles: nuclei 24He
particles: electrons
: photons (more energetic than x-rays) penetrate!
3 Types of Radioactivity
Easily Stopped
Stopped by metal
Radioactive sources
B field into screen
detector
92238U 90
234Th: example
24He recall
: example
Decay Rules
1) Nucleon Number (A) is conserved.2) Atomic Number (Z) 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.
00
A nucleus undergoes decay. Which of the following is FALSE?
1. Nucleon number decreases by 4
2. Neutron number decreases by 2
3. Charge on nucleus increases by 2
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.
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
Nt
N
If the number of radioactive nuclei present is cut in half, how does the activity change?
1) It remains the same
2) It is cut in half
3) It doubles
No. of nuclei present
decay constant
Decays per second, or “activity”
Radioactive decay rates
Preflight 27.8
ACT: Radioactivity
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) 8
Nt
N
No. of nuclei present
decay constant
Decays per second, or “activity”
time
N(t)N0e t N0 2
t
T1/2
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”
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
Summary• Nuclear Reactions
– Nucleon number conserved– Charge conserved– Energy/Momentum conserved– particles = nuclei– - particles = electrons– particles = high-energy photons
• Decays– Half-Life is time for ½ of atoms to decay
N(t)N0e tSurvival:
T1/2
0.693
24He
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