7.9 - Radioactive Decay & Half-Life

Count-rate and activity

Radioactive substances emit radiation from the nuclei of their atoms.

Count-rate

• The count-rate is the number of radiation counts picked up by a detector each second.
• A common detector is a Geiger-Muller tube, connected to a counter that displays the number of counts.
• Photographic film can also detect radiation: it becomes darker the more radiation it's exposed to.

Activity

• The activity is the rate at which a source decays.
• It's measured in becquerels (Bq), where 1 Bq is 1 decay (one nuclear disintegration) per second.
• A larger radioactive sample has a higher activity, because it contains more radioactive nuclei that can decay.

Radioactive decay and half-life

Radioactive decay is random and spontaneous:

• Random - It's impossible to predict which nucleus will decay next, or exactly when any one nucleus will decay.
• Spontaneous - The rate of decay isn't affected by physical conditions like temperature, pressure or chemical bonding.

Why activity falls

• Each time a nucleus decays it becomes more stable, so the number of undecayed radioactive nuclei steadily falls.
• With fewer radioactive nuclei left, the activity (and count-rate) of the sample decreases over time.

Half-life

• The half-life is the time taken for the number of radioactive nuclei in a sample to halve.
• This is also the time taken for the activity (or count-rate) of a sample to halve.
• Each isotope has its own fixed, characteristic half-life.

Half-life and hazard

• Short half-life - Activity falls quickly: high radiation at the start, but the source soon becomes safe.
• Long half-life - Activity falls slowly: smaller amounts of radiation released, but for a very long time, so nearby areas stay exposed.

Background radiation and correcting the count rate

Background radiation is the low-level ionising radiation that's around us all the time.

Natural sources

• Radon gas and radioactive elements in rocks, soil, air, food and building materials.
• Cosmic rays - Radiation reaching Earth from space.

Man-made sources

• Fallout from nuclear weapons testing.
• Medical uses (e.g. X-rays), nuclear power accidents, and radioactive waste.

Correcting for background radiation

1. Measure the background count rate with no source present.
2. Measure the count rate with the source in place.
3. Subtract the background count rate to get the corrected count rate from the source alone.

Finding half-life from a decay graph

A graph of activity (or count-rate, or number of radioactive nuclei) against time curves downwards, becoming less steep as time goes on.

Reading the half-life off the curve

1. Read the initial value off the vertical axis.
2. Work out half of this value.
3. Find the time on the horizontal axis at which the curve reaches that halved value - that time is one half-life.
4. Check by halving again: each successive halving should take the same length of time.

Subtract the background count first

• Before plotting, subtract the background count from every reading.
• If it isn't removed, the calculated half-life will be incorrect.

Worked example - Time to reach a fraction of activity

The half-life of a radioactive sample is 90 minutes. How long does it take for the activity to fall to one quarter of its initial value?

How your background dose varies

• The radiation dose measures the potential harm to the body from radiation exposure.
• It's measured in sieverts (Sv) or millisieverts (mSv), where 1,000 mSv = 1 Sv.

What affects your dose

• Location - Living where more radon gas seeps out of the ground raises the dose. Living at higher altitudes also increases dose because there's less atmosphere to absorb cosmic rays.
• Occupation - Radiographers and nuclear power workers spend more time near radioactive sources. Aircrew receive higher doses from spending time at high altitude.