P4 - Half-Life

What is radioactive decay?

A random process where unstable nuclei emit radiation to become more stable

Can we predict when a specific nucleus will decay?

No, radioactive decay is a random process

What is the definition of half-life (based on nuclei)?

The time it takes for half the unstable nuclei in a sample to decay

What is the definition of half-life (based on count rate)?

The time it takes for the activity (or count rate) of a sample to fall to half its initial value

What is activity?

The rate at which a radioactive source decays, measured in becquerels (Bq)

What is 1 becquerel (1 Bq)?

1 decay per second

What is count rate?

The number of radioactive decays detected per second by a device like a Geiger-Müller tube

Are activity and count rate the same thing?

No, count rate includes effects like background radiation and detector efficiency

How do you find the half-life from a graph of undecayed nuclei vs time?

Find the time it takes for the number of undecayed nuclei to fall to half its starting value

If a sample starts with 1,000 undecayed nuclei and drops to 500 in 10 minutes, what is the half-life?

10 minutes

What happens to the number of undecayed nuclei after each half-life?

It halves

What happens to the count rate after each half-life?

It halves

If an isotope has a half-life of 15 days, how many half-lives is 45 days?

3 half-lives

If the starting count rate is 200 Bq, what is it after 1 half-life?

100 Bq

If the starting count rate is 200 Bq, what is it after 2 half-lives?

50 Bq

If the starting count rate is 200 Bq, what is it after 3 half-lives?

25 Bq

How do you calculate count rate after several half-lives?

Divide the original count rate by 2 for each half-life passed

Formula to calculate remaining count rate after n half-lives

Final count rate = Initial count rate ÷ (2^n)

Why do we use half-life instead of exact decay time?

Because decay is random, half-life gives a statistical average

Does a short half-life mean fast or slow decay?

Fast decay

Does a long half-life mean fast or slow decay?

Slow decay

Why is knowing half-life important in medicine and archaeology?

It helps determine how long a radioactive substance remains active or how old a sample is (e.g. carbon dating)