1. The half-life of the element is 22 years
2. The time taken for 308 g of the sample to decay to 4.8125 g is 132 years
Definition of half-life
Half-life is simply defined as the time taken for half of a material to decay.
1. How to determine the half-life
- Original amount (N₀) = 45 g
- Half of the original amount = 45 / 2 = 22.5 g
From the diagram, the time for 22.5 g is 22 years.
Thus, the half-life of the element is 22 years
2. How to determine the time
i. Determination of the number of half-lives
- Original amount (N₀) = 308 g
- Amount remaining (N) = 4.8125 g
- Number of half-lives (n) =?
2ⁿ = N₀ / N
2ⁿ = 308 / 4.8125
2ⁿ = 64
2ⁿ = 2⁶
n = 6
ii. Determination of the time
- Number of half-lives (n) = 6
- Half-life (t½) = 22 years
t = n × t½
t = 6 × 22
t = 132 years
See attached photo for diagram
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