Transcript Binding Energy1

Overview
A
Z
Recall: Nuclear Physics
6
3
Li
Nucleus = Protons+ Neutrons
nucleons
Z = proton number (atomic number)
Gives chemical properties (and name)
N = neutron number
A = nucleon number (atomic mass number)
Gives you mass density of element
A=N+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
Strong Nuclear Force
Hydrogen atom: Binding energy =13.6eV
(of electron to nucleus)
Coulomb force
proton
electron
neutron
proton
Simplest Nucleus:
Deuteron=neutron+proton
(Isotope of H)
Very strong force
Binding energy of deuteron = 2.2  106 eV or
2.2Mev! That’s around 200,000 times bigger!
# protons = # neutrons
Pauli Principle - neutrons and protons have
spin like electron, and thus ms= 1/2.
n  n p p 
n  n p p 
Can get 4 nucleons into
n=1 state. Energy will
favor N=Z
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.
7
Deuteron Binding Energy
2.2 MeV
ground state
Nuclei have energy level (just like atoms)
energy needed to
remove a neutron from
12C is 18.7 MeV
12C
energy needed to
remove a proton from
12C is 16.0 MeV
energy levels
Note the energy scale is MeV rather than eV
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=(1.67x10-27kg)(3x108 m/s)2=1.50x10-10 J
Proton: mc2 = 938.3MeV
Neutron: mc2= 939.5MeV
Deuteron: mc2 =1875.6MeV
Adding these, get
1877.8MeV
Difference is
Binding energy,
2.2MeV
MDeuteron = MProton + MNeutron – |Binding Energy|
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.
Binding Energy Plot
Iron (Fe) has most binding energy/nucleon. Lighter
have too few nucleons, heavier have too many.
BINDING ENERGY in MeV/nucleon
10
Fission
238
92 U
Fission = Breaking large atoms into small
Fusion = Combining small atoms into large
Which element has the highest binding
energy/nucleon?
•
Neon (Z=10)
•
Iron (Z=26)
•
Iodine (Z=53)
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
3 Types of Radioactivity
B field
into
screen
Radioactive
sources
a particles:
4
2 He
detector
nuclei
b- particles: electrons
Easily Stopped
Stopped by metal
g : photons (more energetic than x-rays) penetrate!
Decay Rules
1) Nucleon Number (A) is conserved.
2) Atomic Number (Z) is conserved.
3) Energy and momentum are conserved.
a: example
238
234
U
92
90Th
a
recall 42 He  a
Nucleon number conserved
Charge conserved
1) 238 = 234 + 4
2) 92 = 90 + 2
b: example
g:
example
1
0
n 11 p  -10e -  00
A
Z
P  P g
*
A
Z
0
0
Needed to conserve
momentum.
A nucleus undergoes a 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
234
90Th
undergoes b
-
decay.
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?
1
238
234
U
92
90Th
2
214
84
3
14
6
4
40
19
a
4
Po210
Pb

82
2 He
C147 N  g
K  4020 P  -10e-  00
Radioactive decay rates
Decays per second,
or “activity”
N
 -N
t
No. of nuclei
present
decay constant
Preflight 27.8
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
ACT: Radioactivity
Decays per second,
or “activity”
N
 -N
t
No. of nuclei
present
decay constant
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
Decay Function
N(t )  N0 e -t  N0 2
time
-
t
T1/2
Radioactivity Quantitatively
Decays per second,
or “activity”
N
 -N
t
No. of nuclei
present
decay constant
Survival:
N(t )  N0 e -t
No. of nuclei
present at time t
No. we started
with at t=0
Instead of base e we can use base 2:
e
-t
2
-
t
T1/2
where
T1/2 
0.693

Half life
Then we can write N(t )  N0 e -t  N0 2
-
t
T1/2
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
a particles = 42 He nuclei
b- particles = electrons
g particles = high-energy photons
Survival:
N(t )  N0 e -t
0.693
T1/2 

• Decays
– Half-Life is time for ½ of atoms to decay