20.4 – Half-life | Physics with Mr Shone

As nuclear decay is a spontaneous random process, we do not know if a particular atom will decay. However, with a large number of atoms we can make predictions about how many will decay within a certain time. This is because each particular nuclide has a fixed half-life.

Definition: Half-Life
Half-life is the time taken for half of the radioactive nuclei of a particular nuclide in any sample to decay.

Example
A student is given a sample of a radioactive element that has a half-life of 5 hours. She thinks the sample will be safe to handle after 10 hours as it will all have decayed. Is she correct? No, she is not correct. 10 hours is two half-lives, meaning that the activity will have dropped to 25% of the original value.

Example
The half-life of iodine-131 is 8 days. Given an initial 12 g of this isotope, how much will be remaining after 24 days? 24 days is 3 half-lives. Amount of iodine-131 present after 3 half-lives have passed will be: 12 ÷ 2 ÷ 2 ÷ 2 = 1.5 g

Example

The half-life of iodine-131 is 8 days.

Given an initial 12 g of this isotope, how much will be remaining after 24 days?

24 days is 3 half-lives.

Amount of iodine-131 present after 3 half-lives have passed will be:

12 ÷ 2 ÷ 2 ÷ 2

= 1.5 g

Example
A radioactive sample has an initial count rate of 3000 counts/s. The count rate drops as the sample decays as shown below. (a) What is the count rate after 6 minutes? 1050 counts/s (b) What is the half-life of this particular nuclide? Time taken to drop from a count rate of 3000 counts/s to 1500 counts/s is 4 minutes.

Example

A radioactive sample has an initial count rate of 3000 counts/s. The count rate drops as the sample decays as shown below.

(a) What is the count rate after 6 minutes?

1050 counts/s

(b) What is the half-life of this particular nuclide?

Time taken to drop from a count rate of 3000 counts/s to 1500 counts/s is 4 minutes.

Links
YouTube Video: Radioactive Decay & Half-Life

2025 Physics Lessons