1. Nuclear Binding, Radioactivity
Physics 102: Lecture 27
Nuclear Binding, Radioactivity
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2. Strong Nuclear Force Hydrogen atom: Binding energy =13.6eV neutron
(of electron to nucleus)
Coulomb force
electron
proton
neutron
proton
Simplest Nucleus: Deuteron=neutron+proton
Very strong force
Binding energy of deuteron = or 2.2Mev! That’s around 200,000 times bigger!

3. Deuterium Binding Energy
2.2 MeV
ground state

5. Nuclei have energy level—just like atoms
energy needed to remove a proton from 12C is 16.0 MeV
energy needed to remove a neutron from 12C is 18.7 MeV
12C energy levels
Note the energy scale is MeV rather than eV

6. Smaller is Bigger! Example Comparing Nuclear and Atomic sizes
Hydrogen Atom: Bohr radius =
Note the TREMENDOUS difference
Nucleus with nucl number A: A
has radius
Example Z
Nucleus is 104 times smaller and binding energy is 105 times larger!

7. Preflight 27.2
Where does the energy released in the nuclear reactions of the sun come from?
covalent bonds between atoms
binding energy of electrons to the nucleus
binding energy of nucleons

9. Binding Energy Example
Einstein’s famous equation E = m c2
Example
proton:
mc2=(1.67x10-27kg)(3x108 m/s)2=1.50x10-10 J
Proton: mc2 = 938.3MeV
Neutron: mc2= 939.5MeV
Adding these, get MeV
Difference is Binding energy, 2.2MeV
Deuteron: mc2 =1875.6MeV
MDeuteron = MProton + MNeutron – |Binding Energy|

10. ACT: Binding Energy Which system “weighs” more?
Two balls attached by a relaxed spring.
Two balls attached by a stretched spring.
They have the same weight.

11. Binding Energy Plot
Iron (Fe) is most binding energy/nucleon. Lighter have too few nucleons, heavier have too many. 10
Fission
Fusion
BINDING ENERGY in MeV/nucleon
Fission = Breaking large atoms into small
Fusion = Combining small atoms into large

13. Preflight 27.3 Which element has the highest binding energy/nucleon?
Neon (Z=10)
Iron (Z=26)
Iodine (Z=53)

14. Preflight 27.4
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
has 56 nucleons
Total B.E  56x9=504 MeV

15. 3 Types of Radioactivity
Radioactive sources
B field into screen
detector
a particles: nuclei
Easily Stopped
b- particles: electrons
Stopped by metal
g : photons (more energetic than x-rays) penetrate!

17. Decay Rules Example g: example Nucleon Number is conserved.
Atomic Number (charge) is conserved.
Energy and momentum are conserved.
: example
recall
238 = Nucleon number conserved
92 = Charge conserved
Comment on preflight only 30% got correct that alpha decay does NOT have charge increase by 2.
: example
Needed to conserve momentum.
g: example

18. Preflight 27.6
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

19. Preflight 27.7 The nucleus undergoes 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.

21. ACT: Decay
Which of the following decays is NOT allowed? 1 2 3 4

22. Preflight 27.8 Decays per second, or “activity”
No. of nuclei present
Decays per second, or “activity”
decay constant
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

23. ACT: Radioactivity Decays per second, or “activity”
No. of nuclei present
Decays per second, or “activity”
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

25. Decay Function
time

26. Radioactivity Quantitatively
No. of nuclei present
Decays per second, or “activity”
decay constant
Survival:
No. of nuclei present at time t
No. we started with at t=0
Instead of base e we can use base 2:
where
Half life
Then we can write

27. You are radioactive! Example
One in 8.3x1011 carbon atoms is 14C which b- decays with a ½ life of 5730 years. Determine # of decays/gram of Carbon.

29. Carbon Dating
We just determined that living organisms should have a decay rate of about 0.23 events/ gram of carbon.
The bones of an ice man are found to have a decay rate of 0.23/ 2 events/gram. We can estimate he died about 6000 years ago.
Example

30. 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

31. Summary Nuclear Reactions Decays Nucleon number conserved
Charge conserved
Energy/Momentum conserved
a particles = nucleii
b- particles = electrons
g particles = high-energy photons
Decays
Half-Life is time for ½ of atoms to decay
Survival:

33. See you next time!
Take a look at Special Relativity in 14 Easy (Hyper)lessons: