Nuclear Physics notes

MDCAT Physics

Nuclear physics deals with the composition and stability of atomic nuclei, radioactive decay, nuclear reactions, and the uses of radiation. It also explains half life, activity, nuclear energy, artificial radioactivity, radiation detection, and medical applications.

Composition of Atomic Nuclei

The nucleus is the small, dense central part of an atom. It contains positively charged protons and neutral neutrons. Protons and neutrons are collectively called nucleons. Electrons move around the nucleus in shells.

The atomic number identifies an element and is represented by Z. It is equal to the number of protons. The mass number is represented by A and is the total number of protons and neutrons.

Nuclear notation is written as A over Z followed by the chemical symbol. Thus, in uranium 235, the atomic number is 92 and the mass number is 235. It contains 92 protons and 143 neutrons.

Atomic number Z = number of protons.
Mass number A = number of protons + number of neutrons.
Number of neutrons N = A minus Z.
A neutral atom has equal numbers of protons and electrons.
Isotopes have the same atomic number but different mass numbers.
Uranium 235 and uranium 238 both have 92 protons. Uranium 238 has 3 more neutrons than uranium 235.
The nucleus contains almost the whole mass of an atom, while most of the atom is empty space.

Nuclear Forces and Mass Energy

Protons repel one another because they have positive charges. However, the nucleus remains together because of the strong nuclear force. This force acts between protons and neutrons over a very short distance.

The four fundamental forces in nature are gravitational force, electromagnetic force, strong nuclear force, and weak nuclear force. Radioactive beta decay is associated with the weak nuclear interaction.

The mass of a bound nucleus is slightly less than the combined mass of its separate nucleons. This difference is called mass defect. It is converted into binding energy according to E = mc².

The strong nuclear force is attractive at nuclear distances and holds nucleons together.
The strong nuclear force is short range and is nearly independent of the charge of the nucleon.
The electromagnetic force causes repulsion between protons.
The four fundamental forces are gravitational, electromagnetic, strong nuclear, and weak nuclear forces.
One atomic mass unit, 1 u, is equivalent to approximately 931 MeV of energy.
Greater binding energy per nucleon generally indicates greater nuclear stability.
In proton and antiproton collision, matter and antimatter can annihilate and produce energy and other particles.

Radioactive Decay and Its Properties

Radioactivity is the spontaneous disintegration of an unstable atomic nucleus. During decay, the nucleus emits alpha particles, beta particles, or gamma rays. The original nucleus is called the parent nucleus, and the resulting nucleus is called the daughter nucleus.

Radioactive decay is a random process for an individual nucleus. It is not possible to predict exactly when one particular nucleus will decay, but the behaviour of a large sample follows a definite law.

Radioactivity is a nuclear phenomenon. Therefore, ordinary physical conditions do not significantly affect it. Changing temperature, pressure, or chemical state does not change the decay rate of a radioactive substance.

Radioactive emission is spontaneous and cannot be stopped by ordinary physical methods.
Radioactive decay is not significantly affected by temperature or pressure.
The rate of disintegration is directly proportional to the number of radioactive atoms present at that instant.
The decay law is written as R = λN, where R is activity, λ is decay constant, and N is the number of undecayed atoms.
The decay constant is the probability per unit time that a nucleus will decay.
Natural radioactivity occurs in unstable nuclei found in nature.
Artificial radioactivity is produced by bombarding stable elements with high energy particles.

Alpha, Beta, and Gamma Radiations

An alpha particle is the nucleus of a helium atom. It contains two protons and two neutrons. Alpha emission changes both the mass number and atomic number of the parent nucleus.

A beta particle is a high speed electron or positron emitted from the nucleus. In ordinary beta minus decay, a neutron changes into a proton, an electron, and an antineutrino. The mass number remains unchanged, while the atomic number increases by one.

Gamma radiation consists of high energy electromagnetic photons. Gamma emission does not change the mass number or atomic number. It usually occurs when a daughter nucleus loses excess energy.

Alpha decay: A decreases by 4 and Z decreases by 2.
Beta minus decay: A remains unchanged and Z increases by 1.
Gamma decay: A and Z both remain unchanged.
Penetrating power increases in the order alpha, beta, gamma.
Ionizing power generally decreases in the order alpha, beta, gamma.
Alpha particles are stopped by paper or the outer layer of skin.
Beta particles can be stopped by a thin sheet of aluminium, while gamma rays require thick shielding such as lead or concrete.
The maximum electron energy in neutron beta decay is approximately 783 keV.

Changes in Nuclear Equations and Decay Series

Nuclear equations must conserve mass number and atomic number. When a particle is emitted, the mass number and atomic number of the daughter nucleus are found by subtracting the corresponding values of the emitted particle.

For example, alpha emission changes a nucleus with mass number A and atomic number Z into a nucleus with mass number A minus 4 and atomic number Z minus 2. Beta minus emission changes Z to Z plus 1 without changing A.

In a decay series, the changes from all emissions are added together. Gamma emission contributes no change to either A or Z.

For alpha particle: mass number = 4 and atomic number = 2.
For beta minus particle: mass number = 0 and atomic number = minus 1 in the emitted particle notation.
For gamma ray: mass number = 0 and atomic number = 0.
For two alpha decays and one beta minus decay, the total change in mass number is minus 8 and the total change in atomic number is minus 3.
A nucleus with A = 180 and Z = 72 undergoing alpha, beta minus, alpha, and gamma decays becomes A = 172 and Z = 69.
Heavy radioactive nuclei may pass through a series of alpha and beta decays and eventually form a stable isotope of lead.
The daughter nucleus may itself be radioactive, producing a decay chain.

Half Life, Decay Constant, and Activity

Half life is the time required for half of the radioactive nuclei in a sample to decay. Equivalently, it is the time in which the activity or the amount of undecayed radioactive material becomes half its initial value.

The number of undecayed nuclei decreases exponentially. After each half life, half of the material present at the beginning of that interval remains. The decay process continues even when only a small amount remains.

The activity of a sample is the number of disintegrations per second. Its SI unit is the becquerel, Bq. An older unit is the curie, Ci.

After 1 half life, the remaining amount is 1/2 of the original amount.
After 2 half lives, the remaining amount is 1/4.
After 3 half lives, the remaining amount is 1/8, so the decayed to undecayed ratio is 7:1 and the undecayed to decayed ratio is 1:7.
After 5 half lives, the remaining amount is 1/32, or approximately 3 percent.
The relation between half life and decay constant is T1/2 = 0.693 divided by λ.
Activity is A = λN and decreases with time.
1 Bq equals 1 disintegration per second.
1 curie equals 3.7 × 10^10 disintegrations per second.

Nuclear Fission, Reactors, and Artificial Radioisotopes

Nuclear fission is the splitting of a heavy nucleus into two smaller nuclei, usually with the release of neutrons and a large amount of energy. The emitted neutrons may cause further fissions, producing a chain reaction.

Uranium 235 can undergo fission when struck by a slow neutron. Natural uranium contains uranium 235 and uranium 238, but uranium 235 is the isotope associated with a sustained slow neutron fission chain reaction.

A nuclear reactor controls the chain reaction and uses the released heat to produce steam. The steam drives turbines connected to generators. Enrico Fermi introduced the first atomic reactor.

Uranium 235 undergoes fission with slow neutrons.
A chain reaction occurs when neutrons from one fission produce further fissions.
A moderator slows down fast neutrons in a reactor.
Control rods absorb neutrons and regulate the chain reaction.
The energy of fission comes from the mass defect of the products.
Artificial radioactive elements or radioisotopes can be made by bombarding stable elements with high energy particles.
Neutrons are used to form many radioisotopes by bombardment because they have no electric charge and can enter nuclei easily.

Biological and Medical Uses of Radiation

Radiation is useful because it can ionize matter, destroy living cells, and be detected from outside an object. Its use requires suitable control because excessive exposure can damage healthy tissues and cause radiation sickness or genetic effects.

In medicine, radioactive tracers help doctors study the function of organs. Radiotherapy uses radiation to destroy cancer cells. Radioisotopes are also used in diagnosis, sterilization, and medical research.

The choice of radiation depends on its penetrating and ionizing powers. Gamma rays can pass through the body and are useful for imaging and treatment. Alpha particles have low penetrating power but strong ionizing power, so they can be useful when directed toward a small internal target.

Radioisotopes are used as tracers to follow chemical and biological processes in the body.
Radiotherapy uses controlled radiation to kill or inhibit cancer cells.
Iodine 131 is used in the diagnosis and treatment of thyroid disorders and has a half life of about 8 days.
Gamma rays are used to sterilize medical instruments and some food products.
Radiation can be used to detect leaks in underground pipes and to measure thickness in industrial materials.
Radiation exposure is reduced by decreasing time, increasing distance, and using suitable shielding.
A Geiger Muller tube, commonly called a GM tube, is an instrument used for detecting and monitoring ionizing radiation.
A radiation detector measures radiation intensity or the number of disintegrations reaching it.

Key terms

Nucleus: The dense central part of an atom containing protons and neutrons.
Nucleon: A proton or neutron present in an atomic nucleus.
Atomic number: The number of protons in a nucleus, represented by Z.
Mass number: The total number of protons and neutrons in a nucleus, represented by A.
Isotopes: Atoms of the same element having the same atomic number but different mass numbers.
Radioactivity: The spontaneous disintegration of an unstable nucleus with the emission of radiation.
Decay constant: The probability per unit time that a particular radioactive nucleus will decay.
Half life: The time required for half of the radioactive nuclei or activity in a sample to disappear.
Activity: The number of nuclear disintegrations occurring per second in a radioactive sample.
Alpha particle: A helium nucleus containing two protons and two neutrons.
Beta particle: A high speed electron or positron emitted during nuclear decay.
Gamma ray: A high energy electromagnetic photon emitted by an excited nucleus.
Mass defect: The difference between the mass of separate nucleons and the mass of the bound nucleus.
Binding energy: The energy required to separate a nucleus completely into its individual nucleons.
Nuclear fission: The splitting of a heavy nucleus into smaller nuclei with the release of energy.
Chain reaction: A continuing reaction in which particles from one nuclear reaction cause further reactions.
Radioisotope: An isotope that has an unstable nucleus and emits radiation.
GM tube: A Geiger Muller tube used to detect and monitor ionizing radiation.

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Physics shortcuts

Comparing distance and displacement

Distance equals the magnitude of displacement only when the particle travels along a straight path without reversing direction.

Check whether the path is straight and one-directional.
If yes, distance = |displacement|.
Example: A particle moves 5 m east in a straight line. Distance = 5 m and displacement magnitude = 5 m.

This shortcut does not apply to a curved path or to motion involving a change of direction.

Projectile range and components

For a projectile launched and landing at the same level, use R = u² sin 2θ/g. Resolve the initial velocity into horizontal and vertical components when needed.

Write ux = u cos θ and uy = u sin θ.
For the same launch and landing level, R = u² sin 2θ/g.
Example: u = 20 m/s, θ = 30°, g = 10 m/s². R = 400 sin 60°/10 = 34.6 m.

The range formula does not apply directly when the projectile lands at a different height.

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