1. Units in Nuclear Physics
Different units are used to describe masses in Nuclear physics
An atomic mass unit (u) is particularly convenient
For particle physicists, it is common to use units of MeV/c2
Distances in nuclear physics are typically around 10-15m = 1 fm
Occasionally called a Fermi, usually called a femtometer
Einstein’s most famous equation is important in nuclear science:

2. Antiparticles For every particle there is an antiparticle
same mass and spin, opposite charge
For some particles, the antiparticle is the same as the particle
Name is usually denoted by putting the word anti- in front of it
Symbol is the same with either charge reversed or a bar on it
Name Symbol Charge Spin Mass (MeV/c2)
Proton p +e ½ 938
Anti-Proton p –e ½ 938
Electron e- –e ½ 0.511
positron e+ +e ½ 0.511
The eta is its own anti-particle. What is its mass and charge?
Insufficient information, insufficient information
Zero, insufficient information
Insufficient information, zero
Zero, Zero

3. Nuclei Three quantities describe a nucleus
The number of protons is called the atomic number Z
The number of neutrons is called N
The number of nucleons is called the atomic mass number A
We normally describe nuclei by specifying which element it is, its Z – value, and its A - value A Z
Which two pieces of information are redundant?
Fe and 56 B) Fe and 26 C) 56 and 26
Hence, the Z – value is often omitted

4. Forces in Nuclei
There are electromagnetic interactions among the protons and neutrons
The only one important for our purposes is the repulsion of protons
There is an additional force, called the nuclear force, the strong nuclear force, or the strong force
It is attractive – protons and neutrons attract each other
It is very strong – much stronger than electric forces
It is short-range – only adjacent nucleons affect each other
The strong force does not depend on charge!

5. Sizes in Nuclei
Thanks to scattering experiments (practice exam II, the conservation of energy problem), we have an upper bound on the size of a nucleus
It turns out that nuclei have sizes on the order of femtometers, and most nuclei are spherical.

6. Binding Energy of a Nucleus
Factors that go into figuring out how stable a nucleus is
Strong nuclear force – each nucleon that is added gets to “bind” to its neighbor
Quantum Mechanics – the Pauli Exclusion Principle
(two nucleons of the same spin
can’t occupy the same space)
Because the nucleons are spin ½, you can fit two into every state
Prefer even number of protons and neutrons
Prefer roughly equal numbers of the two
Electric Force – protons repel each other
This force accumulates as you add more and more protons
Large nuclei don’t like having too many protons
Very large nuclei become unstable

7. Best and Worst Bound Nuclei
Most
Well-bound
Well-bound
High energy
The most stable – lowest energy nuclei – have moderate numbers of nucleons, and a little more than half neutrons
4He is a very well bound nucleus
Very heavy nuclei – like Uranium – tend to also have lots of energy

8. Trends in Stability
Because of the forces involved, there are tends in stability.
For light particles, when the number of protons equals the number of neutrons, the nuclei are more stable
For larger nuclei, a higher proportion of neutrons is required.
The most stable nuclei obey magic numbers: Z or N=2,8,20,28,50,82
This is due to shell filling just like with electrons

9. Binding Energy and mass
The mass of a nuclei is less than the mass of its parts.
There must exist a binding energy, i.e., an energy keeping the nuclei together.
The binding energy is so large that there is a measurable mass difference. (Unlike binding due to other forces!)
Eb(MeV)=(Zmp+Nmn-MA) x MeV/amu
Binding energy per nucleon is the binding energy divided by the mass number

10. Binding Energy

11. Binding Energy
Lithium 7: 3 protons, 3 electrons and 4 neutrons, mass of
Binding energy =(3* )c2+4*( )c2-( )c2
Binding energy= c2=39.246MeV
Binding energy per nucleon=5.6MeV

12. Radioactivity Some substances will decay naturally and emit particles
There are multiple types of radioactive decay: alpha, beta and gamma.
Alpha particles barely penetrate a sheet of paper
Beta particles penetrate a few millimeters of aluminum
Gamma particles penetrate several centimeters of lead!
The rate at which a particular decay process occurs in a radioactive sample is proportional to the number of radioactive nuclei present
Each atom has a probability to decay irregardless of the other nuclei

13. Radioactivity
If N is the number of the radioactive nuclei present then,
This means that the number of nuclei decays exponentially
The rate
The half-life (the time it takes for ½ the nuclei to decay)

14. Radioactivity
Starting with a pure sample of nuclide A which decays, what is the number of atoms of A as a function of time:

15. Radioactivity
The plot below shows activity as a function of time for three samples.
Which sample has the longest half-life?
Which sample has the shortest half-life?

16. Radioactive Dating
A g charcoal sample has a 14C activity of dis/min. A living tree has a 14C activity of 15.3 dis/min per 1.00g. The half-live of 14C is How old is the sample?

17. Alpha-Decay Very heavy nuclei are “crowded” – nucleons want to leave
Although it is possible for them to emit single nucleons, this is very rare
Although it is possible for them to emit large particles, it is easier for them to emit small well-bound particles
Such a particle is a 4He nucleus
Because the 4He nucleus has four nucleons, two of which are protons, Z decreases by 2 and A decreases by 4
The 4He nucleus is also called an  - particle
This process is called alpha decay

18. Beta Decay
A neutron inside a nucleus is spontaneously decays into a proton, an electron, and an antineutrino.
The number of protons changes, so the element changes.
Though energy, momentum, angular momentum, nucleon number, and charge is conserved.
A dominate mechanism for light nuclei.

19. Beta: Electron Capture
Another mechanism for light nuclei decay.
A proton inside a nucleus absorbs an electron, and becomes a neutron
The number of protons changes, so the element changes.
Though energy, momentum, angular momentum, nucleon number, and charge is conserved.

20. Gamma Decay
After a nucleus undergoes a radioactive decay, the nucleus is often in an excited state.
The nucleus can lose the energy by emitting a gamma ray
(high energy photon)