The nucleus consists of protons and neutrons, collectively called nucleons. The number of protons is the atomic number. Protons plus neutrons is the atomic mass number or the nucleon number.

Shorthand notation:4

2He, 2713Al, 1

1H, 23592U

Isotopes are atoms that have the same number of protons, but a different number of neutrons.

126C 13

6C 146C

The radius r of the nucleus depends on the atomic number A.

r ª (1.2 x 10-15 m)A1/3 Nuclear density has nearly the same value for all atoms.

Why doesn’t the nucleus fly apart due to the positive charges? The strong nuclear force holds the nucleus together. This force is independent of charge. It has a limited range of action.

To balance the electrostatic forces as the number of protons increases, more neutrons must be present (more strong nuclear force without more electrostatic force).

Eventually a point is reached where the number of protons cannot be balanced by adding more neutrons. 209

83Bi is the stable nucleus with the most protons.

All atoms with more than 83 protons are unstable and spontaneously break down or rearrange their internal structure.

This spontaneous break down or rearrangement is called radioactivity.

The more stable the nucleus is, the greater the amount of energy needed to break it apart. This is the binding energy of the nucleus.

The mass of a stable nucleus is less than the total mass of the individual particles that make up the nucleus. This difference in mass ∆m is the mass deficit of the nucleus.

The mass deficit is directly related to the binding energy by E = mc2. Binding energy = (Mass deficit)c2 = (∆m)c2

Ex 2 - The mass of a 4

2He nucleus is 6.6447 x 10-27 kg. Find (a) the mass deficit and (b) the binding energy.

The atomic mass unit (u) is often used instead of the kilogram. 1 u = 1.6605 x 10-27 kg

In energy, one atomic mass unit is equal to 1.4924 x 10 -10 J = 9.315 x 108 eV = 931.5 MeV.

The binding energy per nucleon is too low for nuclei with more than 83 protons. That is why these elements are radioactive.

Three kinds of rays are produced by radioactivity: alpha rays, beta rays, and gamma rays.

The production of alpha rays is called alpha decay. An alpha particle is a helium nucleus 4

2He.

23892U ---> 234

90Th + 42He

Alpha decay converts one element into another. This is called transmutation. Energy is released in this change and can be calculated from the loss of mass.

Ex 4 - Determine the energy released when decay converts 238

92U into 23490Th.

The energy released appears as kinetic energy of the two particles except for a small amount released as a gamma ray.

Beta particles are electrons. Beta decay is also an example of transmutation.234

90Th ---> 23491Pa + 0

-1e

This released electron is created when a neutron decays to a proton and an electron.

Ex 6 - Find the energy released when -decay changes 234

90Th into 23491Pa .

In a second kind of decay a positron is emitted when a nuclear proton is converted to a neutron. The mass number is unchanged, but the atomic number decreases by one.

A third type of decay is electron capture where the nucleus captures an electron from outside the nucleus.

An excited nucleus can change to a lower energy state releasing a photon, in this case a gamma ray photon. This does not cause transmutation of the element.

Ex 7 - What is the wavelength of the 0.186 MeV gamma ray photon emitted by radium 226

88Ra?

All of the energy emitted during decay does not end up in the beta particle. Some of the energy goes to another particle called a neutrino.

Neutrinos are mass-less or almost mass-less. They have no charge, and can pass through a light-year of lead without interacting with it.

The emission of neutrinos and particles involves a force called the weak nuclear force. Actually the weak nuclear force and the electrostatic force are one fundamental force, the electroweak force.

The electroweak force, the gravitational force, and the strong nuclear force are the three fundamental forces in nature.

Half-life T1/2 is the time required for one-half of the nuclei present in a sample to disintegrate.

Half-lives range from a fraction of a second to billions of years.

Ex 8 - Suppose 3.0 x 107 radon atoms are trapped in an enclosure. The half-life of radon is 3.83 days. How many radon atoms remain after 31 days?

If the product of a radioactive decay is an unstable isotope, this isotope will go through radioactive decay. This will continue until a stable isotope is reached. This is a radioactive decay series.

In a Geiger counter particles and photons cause a gas to ionize and conduct a current. The degree to which it conducts the charge flow is determined by the level of radiation.

In a cloud chamber, a gas is cooled to the point of condensation. When particles pass through the gas droplets form along the path of the particle.

A bubble chamber contains a liquid just at the point of boiling. The particles leave a trail of bubbles.

A photographic emulsion (film) directly produces a record of the particle’s path.