Nuclear Physics 6.10-6.11

Describe how the alpha-particle scattering experiments provide evidence for the existence, charge and size of the nucleus

• Most of the alpha particles aimed at the gold foil went straight through, and some were deviated through small angles;

• hence, most of the atom is empty space:

• A very small number of alpha particles were scattered through large angles (more than 90°);

• this showed the existence of a tiny positive nucleus,

• the size of the nucleus is about 10^-14 m.

Explain why during the closest approach of an alpha particle (during alpha scattering off a gold nucleus), the gold nucleus has a velocity and the alpha particle does not

• There is a repulsive electrical force between the gold nucleus and the alpha particle;

• linear momentum is conserved because there are no external forces;

• the initial kinetic energy of the alpha particle is transformed into electrical potential energy.

State some of the properties common to all isotopes of an element

• same number of protons

• same number of electrons

• same charge

State quantities conserved in a beta decay

• Charge

• Momentum

• Lepton number

• Baryon number

Describe what happens in a beta-plus decay using the quark model

An up quark transforms into a down quark, plus a positron and an electron-neutrino.

Name the fundamental forces experienced by hadrons (neutrons and protons)

• strong nuclear force

• gravitational force

Describe the nature and range of the three forces acting on protons and neutrons in the nucleus

Gravitational Force

• This force is attractive;

• and is long-ranged.

Strong Nuclear Force

• This force is attractive at larger distances (up to 3 fm) and repulsive at short distances (below 0.5 fm)

• and is short-ranged (of the order of 10^-14 m).

Electrostatic Force

• This force is repulsive between protons and zero between neutrons and protons/neutrons; and is long-ranged.

Activity

Rate of decay of nuclei.

Decay Constant

The probability of decay of a nucleus per unit time.

Describe what is meant by the spontaneous nature of radioactive decay of unstable nuclei

The decay cannot be induced; it occurs without external influence.

Describe what is meant by the random nature of radioactive decay of unstable nuclei

It is impossible to predict when a nucleus will decay.

Name the force responsible for beta decay

The weak nuclear force

Describe carbon-dating

• Living organisms (such as plants) take in carbon (such as CO2) whilst they are alive, and when they die, they stop taking in carbon;

• Some of this carbon will be carbon-14;

• The ratio of carbon-14 to carbon-12 for the dead object is determined;

• The current (today's) ratio of carbon-14 to carbon-12 is determined;

• The age of the sample is found using A = A₀ e^–λt

Explain the major limitations of carbon-dating

• The ratio of carbon-14 to carbon-12 is assumed to be constant;

• The activity of the sample may be comparable to the background activity.

Suggest why the activity of a sample undergoing carbon-dating is measured over a long time period and then averaged

The activity is very small, so a long time is needed to build up enough data.

Explain why the method of carbon-dating is not appropriate for samples that are greater than 10^5 years old

The activity of a very old sample is so low that it cannot be differentiated from the background.

Explain the term binding energy of a nucleus

Minimum energy to separate all protons and neutrons of a nucleus.

Explain why the total mass of the individual nucleons of a particular nucleus is different from the mass of the nucleus

• The mass of the nucleus is less than the total mass of the individual nucleons;

• The nucleus has a binding energy, so energy must be supplied in order to free the nucleons from the nucleus;

• The binding energy is equal to the mass difference (mass defect) x c^2.

Describe the process of induced nuclear fission

• A thermal neutron is absorbed by a massive nucleus;

• the massive nucleus splits into two daughter nuclei and one or more fast moving neutrons.

Explain why nuclei with less than approximately 56 nucleons cannot produce energy by fission

The binding energy per nucleon will decrease for fission, which is impossible unless external energy is supplied.

Name two forms of energy produced in thermonuclear reactions

• Kinetic energy;

• Electromagnetic energy / photons.

• Describe how a nuclear reaction can lead to a chain reaction

The neutrons that are produced during one reaction go on to interact with other fissile nuclei (often uranium-235), causing these nuclei to undergo fission reactions.

Explain the role of fuel rods in a nuclear reactor

These contain the fissile material (often uranium-235).

Explain the purpose of using a moderator in the core of a nuclear reactor

• Fission reactions produce fast moving neutrons;

• the neutrons make collisions with the moderator nuclei and transfer some of their kinetic energy;

• so the moderator slows down the fast moving neutrons;

• and slow moving (thermal) neutrons have a greater probability of causing fission.

Suggest a suitable material which could be used as a moderator in a fission reactor

• Water

• Graphite / Carbon

Explain the purpose of using control rods in the core of a nuclear reactor

• The control rods absorb some of the neutrons;

• The control rods are inserted into the reactor so as to allow on average one neutron from a previous reaction to cause subsequent fission reactions.

Suggest a suitable material which could be used in a control rod in a fission reactor

• Boron;

• Cadmium

Explain what is meant by fusion

• Fusion is the joining together of lighter nuclei in order to make heavier nuclei;

• this process releases energy as the total mass before the reaction is larger than the total mass after the reaction.

Explain why nuclei with more than approximately 56 nucleons cannot produce energy by fusion

The binding energy per nucleon will decrease for fusion, which is impossible unless external energy is supplied.

Explain why a proton must have a very high velocity in order to fuse together with another proton

• As the proton travels towards the other proton, it experiences an electrostatic repulsive force that slows it down;

• The proton needs a very high velocity to get close enough to the second proton for the attractive short range strong nuclear force to have an effect and fuse the two protons together.

Suggest a reason why fusion typically occurs at lower temperatures as low as 10^7 K

• Some nuclei will have a kinetic energy greater than the mean kinetic energy and so will be travelling faster;

• so they will have a larger energy to overcome the electrostatic repulsion, and hence cause fusion.