## AQA GCSE Physics

### Revision Notes

Higher Tier Only

• With each half-life, the activity of a sample decreases by half
• The ratio of remaining radioactive nuclei after a period of time can be calculated in different ways

#### Method 1: Halving Method

• Determine the number of half-lives elapsed
• Divide the number 1 by half for each half-life elapsed
• For example, if 4 half-lives have elapsed:

1 ÷ ½ ÷ ½ ÷ ½ ÷ ½ = 1 / 16

• This is the same as a ratio of 1 remaining : 16 original nuclei, or 1:16

#### Method 2: Raising to a Power

• Determine the number of half-lives elapsed
• Use your calculator to raise ½ to the number of half-lives
• For example, if 4 half-lives have elapsed:

(1/2)4 = 1/16

• This is the same as a ratio of 1 remaining : 16 original nuclei, or 1:16

#### Worked Example

A radioactive sample has a half-life of 3 years. What is the ratio of decayed : original nuclei, after 15 years?

Step 1: Calculate the number of half-lives

• The time period is 15 years
• The half-life is 3 years

15 ÷ 3 = 5

• There have been 5 half-lives

Step 2: Raise 1/2 to the number of half-lives

(1/2)5 = 1/32

• So 1/32 of the original nuclei are remaining

Step 3: Write the ratio correctly

• If 1/32 of the original nuclei are remaining, then 31/32 must have decayed
• Therefore, the ratio is 31 decayed : 32 remaining, or 31:32 ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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