Question

The radioactive isotope 210/84 Po decays by alpha emission.

Answer 1

The half-life of polonium-210, given that it decays from 98.3 micrograms to 12.3 micrograms in 414 days is 138 days

How to determine the number of half-lives

• Original amount (N₀) = 98.3 micrograms
• Amount remaining (N) = 12.3 micrograms
• Number of half-lives (n) =?

2ⁿ = N₀ / N

2ⁿ = 98.3 / 12.3

2ⁿ = 8

2ⁿ = 2³

n = 3

How to determine the half life

• Number of half-lives (n) = 3
• Time (t) = 414 days
• Half-life (t½) = ?

t½ = t / n

t½ = 414 / 3

t½ = 138 days

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Answer 2

The half life of the polonium-210 is 138 days.

What is Half-Life?

The half-life is the time taken for half the sample to decay.

It takes 414 days for 98.3 g of to decay from 98.3 micrograms to 12.3 micrograms.

The fraction of 98.3 that is 12.3 g = 98.3/12.3 = 1/8

The sample has undergone 3 half-lives.

The half-life = 414/3 = 138 days.

In conclusion, it takes 138 days for half the sample to decay.

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