# 28.2.3 Half-Life

### Half-Life Definition

• 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

### Calculating Half-Life

• 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)
• 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

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  ### 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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