Activity decreases over time

Slide along the decay curve: how long does it take to halve?

Time (hours): 6. Activity (kBq): 10. Activity: 10.0 kBq

Slide along the curve. Where does the activity halve?

Physics · Activity and mass

Imagine a pure sample of one isotope, built from equal chunks. Drag to add chunks and watch the mass and the activity move together.

Predict, then check

Two pure samples start with the same activity. Isotope A has a short half-life and isotope B has a long one.

Which sample will have given out most of its radiation sooner?

What you need to know

• Unstable nuclei decay and emit ionising radiation, turning a parent nucleus into a more stable daughter. Stable isotopes do not decay.
• Activity is the number of decays per second. 1 Bq is one decay per second; 1 kBq is 1000 decays per second.
• Have a goA friend counts 4000 decays every second from a sample and announces its activity is 4000 kBq. Fix their number.

  4 kBq

  1 kBq is 1000 decays per second, so 4000 decays per second is 4 kBq. The 'k' means a thousand.

• As a sample decays, fewer unstable nuclei are left, so fewer decays happen each second. Its activity decreases over time.
• In a pure sample of one isotope all the nuclei are identical, so doubling the mass doubles the activity.
• Decay is random: you cannot predict when one particular nucleus will decay, but you can predict how long half a sample takes.
• Have a goA fortune teller offers to name the exact second one particular nucleus in your sample will decay. Worth the money?

  No. That moment cannot be predicted. How long half the sample takes can be.

  Decay is random for each nucleus, but a whole sample behaves predictably, so the useful prediction is for half the sample.

• Half-life is the time for half the nuclei to decay, or for the activity to fall to half its initial value.
• Have a goA sample starts at 100 kBq and its half-life is 5 minutes. What is its activity after exactly 5 minutes?

  50 kBq

  One half-life is the time for the activity to fall to half its initial value, and half of 100 is 50.

• Each isotope has its own half-life, always the same. It is not half the time for all the nuclei to decay.
• On a decay curve, find the time for the activity to halve from any start. Averaging several starts is more reliable.
• Activity keeps halving in equal times: a half, then a quarter, then an eighth. Count the half-lives, then halve that many times.
• Isotopes with short half-lives decay quickly, emitting most of their radiation over a short period of time.

The big picture

A radioactive sample's activity falls because its unstable nuclei decay and fewer are left. Whatever activity you start from, it halves in the same time, called the half-life, so the activity goes down by a half, then a quarter, then an eighth.

⚠ Watch out

Thinking half-life is half the time for all the nuclei to decay, or that nothing is left after two half-lives. Each half-life only halves what is left, so the activity goes ½, then ¼, then ⅛.

Memory hook

A half, then a quarter, then an eighth. Each half-life only halves what is left, so it never drops straight to zero.

Check yourself

In two sentences, explain to a friend why a radioactive sample's activity falls even though nobody touches it, and why 'half-life is half the time for everything to decay' is wrong.