3.5: Nuclear decay

It is emitted from the nucleus of an unstable isotope during a nuclear decay process.

Atoms of the same element which have the same number of protons but different numbers of neutrons.

The stability of an isotope.

A fast moving helium nucleus that is usually emitted from the decay of a heavy isotope

The parent isotope is converted into a new a dughter element with atomic number 2 lower and mass number 4 lower than the parent isotope.

A fast moving electron emitted from a nucleus.

A neutron inside the nucleus converts into a proton plus an electron.
The electron is then emitted.
The atomic number of the parent isotope increases by 1 and the mass number doesn't change.

A high-energy, short-wavelength electromagnetic wave.

The wave is emmited from an excited nucleus or accompanies other types of decay.
Atomic and mass numbers are unaffected.

It knocks electrons out of atoms or molecules.

They can be highly reactive and go on to react with other nearby molecules.

Ionised DNA can lead to the production of cancerous cells.

They have electric charges of 2+ and can ionise molecules via electrostatic attraction without making direct contact.

Each ionisation event robs the alpha particle of energy causing it to slow down.
Slower moving alpha particle are more ionising because there is greater time for the ionising electrostatic interaction to occur.
Alpha particles become more ionising with penetration depth.

A sheet of paper or a few centimetres of air.

They have a negative charge and are much less massive than alpha particles.
They must make close contact with a molecule to cause ionisation.

They must make close contact with a molcules to cause ionisation.
This makes them less ionising and they lose less energy and therefore lose less speed.
They don't become more ionising with penetration depth.

A few mm of aluminium or a few metres of air.

Gamma rays have no mass or charge.
They are less ionising than alpha or beta rays but are more penetrating.

15cm of lead or 1m of concrete.

R = 1/d^2
R = count rate
d = distance from source

By placing a geiger counter between a radioactive source and various absorbers.

They are weakly deflected towards the negative side of an electric field.

They are deflected towards the positive side of an electric field.

They have no charge so are not deflected in an electric field.

Radioactive isotopes in the environment.

They contain radioactive elements.
These are found in buildings due to the materials used.
Food and drink can emit radiation as these are derived from rocks and soil.

Radon gas.

Cosmic rays are highly energetic particles emitted by the sun, most of which is absorbed by the atmosphere.

X rays used in medical imaging.

Nuclear power and nuclear testing.

Background radiation levels are low, therefore a long time period must be used for background measurement and converted to counts per minute.

The becquerel = 1 decay per second with units of s^-1

The time taken for half of the radioactive nuclei in a sample to decay.

The number of disintegrations per scond is directly proportional to the number of radioactive nuclei in a sample.
A α N

A = λN
A = -ΔN/Δt
ΔN/Δt = -λN
A = The number of disintegrations per second
N = The number of radioactive nuclei in a sample
λ= The decay constant
t = time

N = N0e^-λt
N = Number of nuclei at time = t
N0 = Number of nuclei initially
λ= Decay constant
t = Time

N = N0e^-λt
multiply both sides by λ
λN = λN0e^-λt
Since A = λN
A = A0e^-λt
A = Activity at time = t
A0 = Initial activity

When the time for a sample reaches the half life t = T(1/2)
The activity of the sample has then fallen from, A0 to 1/2A0
After one half-life we can write, 1/2A0 = A0e^-λT(1/2)
A0 cancels, 1/2 = e^-λT(1/2)
Reciprocate, 2 = e^λT(1/2)
Take logs, ln2 = λT(1/2)
Rearrange, λ= ln2/T(1/2)

1/2^n
n = Number of half-lives

A = A0/2^n
A = Activity after n half lives
A0 = Initial activity
n = Number of half lives

N = N0/2^n
N = Number of nuclei remaining after n half lives
N0 = Initial number of nuclei
n = Number of half lives