Question

The table shows the amount of radioactive element remaining in a sample over a period of time.
Radioactive Decay Rate
Amount of Radioactive Sample(grams)
45.0
31.8
22.5
15.9
11.3
Time(years)
0
11
22
33
44
Part 1: What is the half-life of the element? Explain how you determined this.
Part 2: How long would it take 308 g of the sample to decay to 4.8125 grams? Show your work or explain your answer

Answer 1

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

• Time (t) =?

t = n × t½

t = 6 × 22

t = 132 years

See attached photo for diagram

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