The time taken for the isotope to decay is 46 million years.
We'll begin by calculating the number of half-lives that has elapsed. This can be obtained as follow:
- Original amount (N₀) = 50.25 g
- Amount remaining (N) = 16.75
- Number of half-lives (n) =?
2ⁿ = N₀ / N
2ⁿ = N₀ / N
2ⁿ = 50.25 / 16.75
2ⁿ = 3
Take the log of both side
Log 2ⁿ = 3
nLog 2 = Log 3
Divide both side by log 2
n = Log 3 / Log 2
n = 2
Finally, we shall determine the time.
- Half-life (t½) = 23 million years
- Number of half-lives (n) = 2
t = n × t½
t = 2 × 23
t = 46 million years
Learn more about half-life: brainly.com/question/25927447
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