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)
- 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
- 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