The time (in years) taken for only 10 mg to remain is 14.84 billion years
Data obtained from the question
- Original amount (N₀) = 100 mg
- Half-life (t½) = 4.47 billion years
- Amount remaining (N) = 10 mg
- Time (t) =?
Determination of the number of half-lives that has elapsed
- Original amount (N₀) = 100 mg
- Amount remaining (N) = 10 mg
- Number of half-lives (n) =?
N × 2ⁿ = N₀
10 × 2ⁿ = 100
Divide both side by 10
2ⁿ = 100 / 10
2ⁿ = 10
Take the log of both side
Log 2ⁿ = Log 10
nLog 2 = Log 10
Divide both side by Log 2
n = Log 10 / Log 2
n = 3.32
How to determine the time (in years)
- Half-life (t½) = 4.47 billion years
- Number of half-lives (n) = 3.32
- Time (t) =?
t = n × t½
t = 3.32 × 4.47
t = 14.84 billion years
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