# Half-Life(OCR A Level Physics)

Author

Katie M

Expertise

Physics

## Half-Life

• Half life is defined as:

The time taken for the initial number of nuclei to reduce by half

• This means when a time equal to the half-life has passed, the activity of the sample will also half
• This is because activity is proportional to the number of undecayed nuclei, A ∝ N

When a time equal to the half-life passes, the activity falls by half, when two half-lives pass, the activity falls by another half (which is a quarter of the initial value)

## Determining the Half-Life of an Isotope

• To find an expression for half-life, start with the equation for exponential decay:

N = N0e–λt

• Where:
• N = number of nuclei remaining in a sample
• N0 = the initial number of undecayed nuclei (when t = 0)
• λ = decay constant (s-1)
• t = time interval (s)

• When time t is equal to the half-life t½, the activity N of the sample will be half of its original value, so N = ½ N0

• The formula can then be derived as follows:

• Therefore, half-life t½ can be calculated using the equation:

• This equation shows that half-life t½ and the radioactive decay rate constant λ are inversely proportional
• Therefore, the shorter the half-life, the larger the decay constant and the faster the decay

#### Worked example

Strontium-90 is a radioactive isotope with a half-life of 28.0 years. A sample of Strontium-90 has an activity of 6.4 × 109 Bq.Calculate the decay constant λ, in s–1, of Strontium-90.

Step 1: Convert the half-life into seconds

28 years = 28 × 365 × 24 × 60 × 60 = 8.83 × 108 s

Step 2: Write the equation for half-life

Step 3: Rearrange for λ and calculate

#### Exam Tip

Make sure you are confident with the meanings of all the definitions and symbols in this unit. It is easy to get confused when completing an examination question.

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### Author:Katie M

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.