Question

Element X decays radioactively with a half life of 10 minutes. If there are 110 grams of
Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 18 grams?

Answer 1

The time taken to the nearest tenth for the element X to decay from 110 g to 18 g is 26.1 mins

How to determine the number of half-lives

• Original amount (N₀) = 110g
• Amount remaining (N) = 18  g
• Number of half-lives (n) =?

2ⁿ = N₀ / N

2ⁿ = 110 / 18

2ⁿ = 55/9

Take the log of both side

Log 2ⁿ = Log (55/9)

nLog 2 = Log (55/9)

Divide both side by Log 2

n = Log (55/9) ÷ Log 2

n = 2.61

How to determine the time

• Number of half-lives (n) = 2.61
• Half-life (t½) = 10 mins

• Time (t) =?

t = n × t½

t = 2.61 × 10

t = 26.1 mins

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