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Element X decays radioactively with a half life of 13 minutes. If there are 560 grams
of Element X, how long, to the nearest tenth of a minute, would it take the element to
decay to 150 grams?

Sagot :

Eduard22sly

The time taken for the element X to decay from 560 grams to 150 grams is 24.7 mins

How to determine the number of half-lives

  • Original amount (N₀) = 560 g
  • Amount remaining (N) = 150 g
  • Number of half-lives (n) =?

2ⁿ = N₀ / N

2ⁿ = 560 / 150

2ⁿ = 3.73

Take the log of both side

Log 2ⁿ = Log 3.73

nLog 2 = Log 3.73

Divide both side by Log 2

n = Log 3.73 / Log 2

n = 1.9

How to determine the time

  • Number of half-lives (n) = 1.9
  • Half-life (t½) = 13 mins
  • Time (t) =?

t = n × t½

t = 1.9 × 13

t = 24.7 mins

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