Physics 222, November 26
Key Concepts:
•Nuclear properties •Nuclear decay •Nuclear models •Nuclear energy Nuclear properties A nucleus is a quantum particle made from protons and neutrons. We cannot track these particles inside the nucleus.
A Notation: ZX A = # of nucleons, Z = # of protons, X = chemical symbol
1/3 -15 Radius: R = R0A R0 = 1.2*10 m
Classical picture What is the approximate mass number (number of nucleons) of a nucleus whose radius is measured to be 6*10-15 m?
1. 6 2. 125 3. 256 4. 80 5. 64 Interactions The long-range electrostatic force cause protons to repel each other. The short range nuclear or strong force holds the nucleus together. It is charge independent and acts equally on neutrons and protons.
Range of nuclear force: D0 ~ 4 proton diameters
The nuclear binding energy is the amount of energy needed to completely separate a nucleus into its component neutrons and protons.
Short range nuclear force no super large nuclei Protons are repelled by all the other protons.
Nucleons are attracted only by neighbors within D0.
In super large nuclei: Electrostatic repulsion > nuclear attraction
Does this graph make sense? Consider both the nuclear and the electrostatic interaction. A proton in a very large nucleus
1. attracts all other protons. 2. repels all other protons. 3. repels all neutrons. 4. attracts some protons and repels others. 5. attracts some neutrons and repels others. The most stable nuclei all have around 60 nucleons. Why?
1. Their ration of protons to neutrons is much smaller than that of the large nuclei, like, for example Uranium. 2. They have a diameter about equal to the range of the nuclear force. 3. They have just the right amount of negatively charged electrons to cancel the repulsion of the positively charged protons. 4. They are made of Helium nuclei. What is the definition of the of nuclear binding energy?
1. It is the amount of energy needed to remove the most loosely bound electron from an atom. 2. It is the amount of energy needed to remove the most loosely bound proton from a nucleus. 3. It is the amount of energy needed to completely separate a nucleus into its component neutrons and protons. 4. It is the amount of energy needed to remove all electrons from an atom. 5. It is the amount of energy needed to remove all electrons from an atom and then take the nucleus apart. Nuclear models
Shell model: Confinement leads to energy quantization.
Energy levels can be grouped into shells. There are shells for protons and for neutrons. Nucleons fill the lowest available energy levels allowed by the Pauli exclusion principle.
In stable nuclei the highest energy protons have roughly the same total energy as the highest energy neutrons.
This leads to the “valley of stability”. Magic numbers
The Pauli exclusion principle is responsible for a shell structure in nuclei, similar to the shell structure in atomic physics, where the noble gases have especially large ionization energies.
Nuclei with magic neutron number N = 2, 8, 20, 28, 50, 82, 126 or magic proton number Z = 2, 8, 20, 28, 50, 82 have a larger binding energy per nucleon than neighboring nuclei and are called magic. When N and Z are both magic the binding energy per nucleon is especially large, and the nuclei are called doubly magic. 16 17 18 8O, 8O, and 8O are all stable oxygen isotopes. Which one likely has the largest binding energy per nucleon?
16 1. 8O because it is doubly magic. 18 2. 8O because it has the smallest proton to neutron ratio. 17 3. 8O because it lies between two stable isotopes. 4. They all have the same binding energy per nucleon. The long-range electrostatic repulsion between protons limits the size of stable nuclei. Why are there no large nuclei consisting only of neutrons, which do not repel each other?
1. The nuclear force acting on protons is stronger than that acting on neutrons, so neutrons would not be bound. 2. The Pauli exclusion principle would require the neutrons to occupy very high energy states, yielding the nucleus unstable. 3. Nuclei are in the center of atoms, and the atomic electrons would not be bound if there were no protons in the nucleus. E = mc2 Binding energy formula
Using nuclear masses: 2 B(Z,N) = c (Z*mp + N*mn - Mnuc(Z,N)) (nuclear masses are usually given in units of MeV/c2)
Or, using atomic masses:
2 B(Z,N) = c (Z*mH + N*mn - Matom(Z,N)) (atomic masses are usually given in atomic mass units u)
1 u = 931.494 MeV/c2 On a balance scale, you put 2 neutrons and 1 proton on one side and you put a tritium nucleus (3H) on the other. Which side weighs more?
1. The two neutrons and 1 proton. 2. The tritium nucleus. 3. Both sides weigh the same. 4. It depends on the specific tritium isotope. Nuclear decay Decay is a quantum process. All we can know is the decay probability. decay constant: λ = decay probability per unit time mean lifetime: τ = 1/λ half-life: t1/2 = τ ln2 = ln2/λ The half-life is the time it takes for half the nuclei to decay.
# of nuclei left after time t: N(t) = N0exp(-λt) decay rate at time t: R(t) = R0exp(-λt) Decay modes: alpha decay:
gamma decay:
beta decay: You have 16 kg of a radioactive sample with a certain half-life of 15 years. How much is left after 45 years?
Hint: How many half-lives have elapsed?
1. 8 kg 2. 4 kg 3. 2kg 4. 1kg 5. nothing 222Rn (Radon) is an unstable nucleus which alpha decays. The resulting nucleus is
1. 222Pb 2. 218Po 3. 214Pb 4. 218Bi 5. 220Po Radionuclides used in PET scanning are typically isotopes with short half-lives, for example carbon-11 (~20 min). Carbon-11 decays, and a Boron-11 nucleus is left behind. What type of decay is this?
1. Alpha decay 2. Beta plus decay 3. Beta minus decay 4. Gamma decay 5. Proton emission 6. Neutron emission Nuclear energy
E = mc2: Whenever a system looses energy, it looses mass. Energy Source: Chemical Fission Fusion Efficiency (E/mc2): 3 * 10-8% 0.002% 0.4% How does the total mass of the fission fragments compare to the mass of the original nucleus in a fission reaction?
1. The fission fragments have more mass than the original nucleus. 2. The fission fragments have less mass than the original nucleus. 3. The fission fragments have the same mass as the original nucleus. 4. Not enough information is given to decide. How does the binding energy per nucleon of a fusion product compare to that of the pieces that combined to form it? 1. The product has a greater binding energy per nucleon than the pieces. 2. The product has less binding energy per nucleon than the pieces. 3. The product has the same binding energy per nucleon than the pieces. 4. It depends on which exact reaction, i.e. on which pieces.