1. Nuclear Binding, Radioactivity
Physics 1161: Pre-Lecture 25
Nuclear Binding, Radioactivity 1

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

4. Nuclei have energy levels — 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

5. 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!

6. 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|

7. 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

8. 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! 26

9. 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
: example
Needed to conserve momentum.
g: example

10. Decay Function
time

11. 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

12. 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.

13. 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: