Nuclear Physics Main Page 

General Information 

Nuclear physics had its start in 1896 when Henri Becquerel discovered radioactivity in uranium.

Radiation was later determined to be of three types, alpha. beta, and gamma rays.

It was determined that most of the mass of an atom was located near its center.  The area where most of the mass is located is called the nucleus.

Since all the protons are considered to be in the nucleus, they should repel each other due to the fact that all protons have a positive charge.  The concept of the nuclear force was developed to solve this problem.

The nuclear force seems to be very strong at distances of less than 10-14 meters and it is zero at greater distances

When working with these small distances the femtometer, or fermi is often used.

Properties of Nuclei

Nuclei are composed of protons and neutrons, with the exception of the common hydrogen nucleus which contains only one proton.

A few terms are used in the description of the nucleus.

Atomic number ( Z ) = number of protons in the nucleus

Neutron number ( N ) = number of neutrons in the nucleus

Mass number ( A ) = number of nucleons in the nucleus

Nucleons = generic term for protons or neutrons

All nuclei of an element must contain the exact same number of protons, but they may contain a different number of neutronsNuclei of the same element that have different numbers of neutrons are called isotopes.

Mass

The unified mass unit, with symbol 'u', is often used when discussing atomic masses.  This is defined such that 1 atom of Carbon-12 has a mass of 12 u.

1u = 1.60217733 x10-19 kg = 931.494 MeV/c2

Since mass can be converted into energy using E=mc2 we can express mass in terms of energy as shown above in the values shown for the unified mass unit.

Charge

The proton has a charge of +e and the electron has a charge of -e, while the neutron has a charge of cipherNeutrons are harder to detect because they have a charge of zero.

Size of Nuclei 

Mr. Rutherford studied the size of nuclei.  He used the principle of conservation of energy for his studies.  he shot alpha particles head-on into various nuclei where they were repelled by Coulomb repulsion.

Density of Nuclei

The nucleus of an atom is very dense.  It seems to be about 2.3 x 1017 kg/m3 or 2.3 x 1014 g/cm3.  All nuclei seem to have about the same density.

Nuclear Force

The nuclear force is a very strong force that holds the nucleus together.  Without this nuclear force the electrostatic forces of the protons would cause the protons to be repelled, thus causing the nucleus to fly apart.  The nuclear force is a very short range force that extends only to a distance of up to about 2 femtometers.  This nuclear force seems to act between all nuclear particles.  While the Coulomb forces repel the protons, the nuclear force attracts them and keeps them together.  It works for pairs of protons, pairs of neutrons, and for a neutron and a proton. The nuclear force seems to be almost  independent of the charges involved.

Light nuclei are most stable when the number of neutrons and the number of protons are about the same.  This can be stated as  being when N = Z. Larger nuclei are stable when there are more neutrons than protons which can be stated as being when N > Z..

Elements with more than 83 protons are not stable.  They decay over time.

Binding Energy

The nucleus has a total mass that is always a bit less than the sum of the masses of its nucleons.  Since mass and energy are related and can be interchanged we can state that the total energy of the nucleus is less than the sum of the energy of all the nucleons in the nucleus.  The binding energy is is the difference between  the total energy of the nucleons by themselves and the total energy of the nucleus.

To break apart the nucleus an amount of energy equal to the binding energy must be added to the nucleus.

A binding energy of zero would allow a nucleus to break apart without the addition of any additional energy.  This would not be a good thing.

The most stable nuclei are those with the highest binding energy.  The average binding energy of all the nuclei is about 8 MeV.  When the mass number (A)  is about 60 the binding energy is at its maximum.

Radioactivity

Radioactivity is the spontaneous emission of radiation.

Radioactivity was discovered in 1896 by Becquerel when he discovered that uranium  gave off an invisible radiation that caused photographic plates to darken even when the plate was protected from light.  This, while bad for the photographic plates, was an important discovery for science.

This discovery led to the discovery that other substances also gave off this invisible radiation that could cause the ruination of photographic plates.

Marie and Pierre Curie studied radioactivity and their experiments resulted in the discover of two unknown radioactive elements which came to be known as radium and polonium.

Additional studies by Rutherford indicated that radioactivity was caused by the disintegration of unstable nuclei.  This disintegration is called decay.

Radioactive substances can give of three types of radiation. They are:

    1) Alpha particles

    2) Beta particles

    3) Gamma rays

These various types of radiation can be separated by using a magnetic field to deflect them and allowing them to hit photographic film to capture the record. Alpha particles are deflected in one direction, beta particles (electrons) in the other direction, and the gamma rays go straight ahead.  If the beta particles contain a positron it will be deflected in the same direction as the the alpha particles.

Alpha Particles

An alpha particle is a helium nuclei which contains two protons and two neutronsAlpha particles can barely pass through a sheet of paper.  Alpha particles have a positive charge since thy have two protons.

Beta Particles

Beta particles are either electrons or positrons.  Beta particles can penetrate a few millimeters of aluminum. The beta particle will have a negative charge if it is an electron but it will have a positive charge if it is a positron.

Gamma rays

Gamma rays are actually high energy photons. Gamma rays can penetrate several centimeters of lead.  The gamma ray is not deflected by the electromagnetic field because it has no charge.

Positron

A positron is, for all practicable purposes, an electron with a positive charge.  It is considered to be the antiparticle of the electron.  While e- is used to indicate an electron the symbol e+ is used to designate the positron.

Decay Constant  

A radioactive substance that contains N radioactive nuclei at some instant in time will decay over time at a rate  that is proportional to N. 

∆N/∆t is proportional to N therefore ∆xN = -λN∆t

where λ is the constant for a specific isotope called the decay constant.  

A large value of λ causes rapid decay while a small value of λ results in a slow decay.

Decay Rate

The decay rate is also called the activity.  It is defined as the number of decays per second.

Decay rate = R = ∆N/∆t = λN 

The number of nuclei left after a period of time is given by 

N = N0 e-λt where

N0 is the original number of nuclei at time = 0 
e = Euler's constant or 2.718281828 
λ is the decay constant for an isotope
t = time in seconds 

 

Half-Life

The half-life of a radioactive substance is the time it takes for half of the radioactive nuclei to decay.

Units of Radioactive Decay

Radioactive decay can be measured in curies or in becquerels.

Curie

Becquerel