Nuclear Decay

Beta Decay

Nuclear decay refers to the changes in unstable isotopes as they change to other more stable isotopes with the release of particles and energy in the form of radiation.

Beta decay happens to small nuclei with an unstable ratio of neutrons to protons. For smaller elements, the ideal stable ratio is between 1:1 to 1.5:1 neutron to protons. Where the ratio is too far from the ideal the excess particles are converted and radiation is also released.

Beta negative decay ____β-

Where an isotope has too many neutrons compared to protons, the excess neutrons are converted to protons by emitting an electron.


146C - Carbon-14 has 6 protons, but 8 neutrons. (7 of each is a more stable configuration).

A neutron is converted to a proton to give a 1:1 ration. However, an atom with 7 protons is no longer carbon, it is nitrogen. An electron is emitted in the process of the change.

146C _→ 147_N + e-

Beta negative decay ____β+

Where an isotope has too many protons compared to neutrons, the excess protons are converted to neutrons by emitting a positron, (a positive equivalent of an electron).


106_C _- Carbon(10) has 6 protons, but only 4 neutrons, this large difference also results in this being a very unstable isotope.

106C _ → 105_B + e+

Alpha Decay

Alpha α

Alpha decay occurs where larger nuclei have an excess of neutrons, they emit 2 protons and 2 neutrons to reduce the overall binding energy to proton repulsion imbalance in the nucleus. Often gamma radiation is emitted in this form of decay too.


Uranium235 converts to Thorium231 : 23592U32190Th + 42He+↗ + ɣ

Alpha decay is associated with larger atomic nuclei, the products of alpha decay are often unstable radioactive isotopes that undergo further, beta or alpha decay over a sequence of changes until smaller more stable isotopes are produced. Uranium decays over a long period of time, and numerous changes, to eventually form a stable isotope of lead.

Nuclear Decay, figure 1

Decay sequence of uranium to lead via alpha and beta decay.

Nuclear Equations

The changes that take place in the nuclei of isotopes as they undergo nuclear decay can be summaries by the following model equations.

Key :

A - atomic mass (number of protons + neutrons)

N - atomic number (number of protons)

X - element symbol of initial isotope

Y - element symbol of product isotope

42He+ - helium nuclei (alpha radiation)

e-_ -electron, e_+_ - positron_

_ɣ - gamma radiation _

no_ - neutron_

Beta negative decay

ANX _→ _ __A__N+1__Y +_ e_-_ _↗ Mass remains unchanged, but the atomic number increased by 1.

Beta positive decay

ANX _→ _A__N-1__Y +_ e_+↗ Mass remains unchanged, but atomic number decrease by 1.

__Alpha Decay __

ANXA-4N-2Y + 42He+ ↗ (+ ɣ) Mass decreases by 4, the atomic number decreases by 2.

Neutron decay

ANXA-2NX + 2no The mass decreases by the number of neutrons lost which can be 2 or 3.

Half Lives

As nuclear decay occurs the isotopes change their configurations and form new elements. Carbon-14 decays to become Nitrogen-14. This results in the gradual loss of mass of the original element.

When an individual nucleus will undergo decay cannot be predicted, it is a random event. It is possible, however, to measure the length of time it takes for a mass of an isotope to reduce by half. This is done by measuring the time for the radioactivity level to reduce by 50%. This period of time is known as the half-life, (t1/2).

The more unstable an isotope is the shorter its half-life.

Nuclear Decay, figure 1

Carbon-14 is a reasonably stable isotope and has a half-life of 5730 years, so 1 kg of Carbon-14 would become ½ kg of Carbon-14 over 5730 years.

Carbon-10 is very unstable and has a half-life of about 20 seconds. 1 kg of Carbon-10 becomes ½ kg in 19.29 seconds.

1 kg of Uranium-235 will take 703.8 million years to decay to ½ kg.

Uranium-235 emits high energy gamma radiation and alpha particles and is a very dangerous substance. It is used in nuclear power and is part of the waste from a nuclear reactor. The long half-life means it remains a highly dangerous substance for a long time.

Calculating half lives

A radioactive isotope is found to produce 200 Bq of radiation. The level of radiation is measured again 1 hour later and the reading has dropped to 25 Bq. What is the half-life of this isotope?

  1. Work out how many times the reading has halved. 200 - 100 -50- 25. Three times.
  2. Divide the time for the decrease by the number of half-lives. 60 minutes ÷ 3 gives a half-life of 20 minutes.


Alpha Radiation

Alpha radiation is used in domestic smoke detectors. A small amount of americium 241 is used to create a beam of alpha particles into an ionizing chamber. As long as there is no smoke in the chamber the changed alpha particle complete the circuit and the alarm will not sounds. However, once smoke enters the chamber the large slow moving alpha particles are deflected and the circuit is broken, setting off the alarm.

Nuclear Decay, figure 1

Alpha radiation is suitable for this application because it is easily deflected by the smoke particle and it is safe to have in the home on account of the low penetration power of the radiation. It can not escape the plastic container it is held in.

Beta Radiation

Due to its higher penetration power, beta radiation is used to measuring and controlling the production of paper and steel sheets. A beam of beta radiation is aimed at the sheet being rolled. Below the sheet is a detector if the rate of detection varies from a specified amount the detector adjusts the roller pressure to maintain a constant end product.

Nuclear Decay, figure 2

Gamma Radiation

Gamma radiation has the potential to kill, it is this property that is put to use in several ways.

  1. Irradiation of food to kill bacteria and fungi. This process is used on many soft fruits and vegetables once packed and prior to shipping. It gives the food a greater shelf life, which is essential in moving perishable goods from country to country.
  2. Radiotherapy; in this application, a targeted beam of radiation is aimed at a cancer tumour, to kill the cancerous cells Alternatively a small sample of the radioactive isotope emitting the gamma radiation can be embedded into a tumour.


The degree of risk from a radioactive source is very variable. Many radioactive materials are a natural part of the background radiation we are exposed to all the time. These do not have any noticeable effect on health. People’s occupations can also have an influence on the degree of risk of exposure to radiation.

Irradiation: exposure to a source of radiation and the absorption of the energy by the body tissues. The energy of the radiation comes into contact with the body tissue, but the material does not.

Contamination: The body comes into direct physical contact with the radioactive material. Normally this means some os transferred and stays on the body or clothing etc.

Contamination can be very serious as it means the object or person is continually exposed to the radiation. The contaminated material will have to have the radioactive material physically removed.

The degree of risk in both cases will depend on the type of radiation and the amount of exposure.

People working with radioactive materials in places like hospitals or in nuclear power plants have to be monitored to measure their exposure and often wear protective clothing to limit both contamination and irradiation.

A radiographer in a hospital has to wear a lead lined apron to protect them from irradiation. They also operate the equipment from behind a lead shielded partition. Their exposure is monitored by analysing the radiation absorbed by a strip of film enclosed in a badge.

A PET scanner in a hospital can allow a doctor to examine the internal workings of a patient. The patient is given a radioactive isotope to drink or it might be injected into the blood. The Scanner can detect this beta radiation and follow its movement. The source has a very short half-life, often this is Carbon 11.Explain why a beta source is required for this application and why it is an advantage for it to have a short half-life.
Your answer should include: penetrate / body / tissues / material / decay / quickly
Explanation: A beta source can penetrate the body tissues so the scanner can detect them. Alpha would not be able to escape the body and gamma would be too dangerous to the patient. The short half-life means the material will decay quickly reducing the risk of irradiation to the patient.
Explain the differences and similarities between beta positive and beta negative decay.
Your answer should include: imbalance / neutron / loss / proton / neutron / becoming / proton
Explanation: Both result from an imbalance in the neutron to proton ratios in small nuclei. Beta positive results in the loss of a proton to become a neutron with the emission of a positron. Beta negative results in a neutron becoming a proton with the emission of an electron.
If a sample of a radioactive material has a measured count of 500 Bq at time zero, and it drops to 125 in 3 days what is its half life?
Explanation: 2 half lives in 3 days so halflife is 1.5 days.