Half life of the isotope is 4.57 x 102 years.
The time it takes for half of an unstable nucleus to go through its decay process is known as its half-life. Half-lives for various substances vary. For instance, because carbon-10 has a half-life of just 19 seconds, it is not found in nature.
Isotope of Americium given : ²⁴¹₉₅Am
Percentage decay = 85%
Remaining fraction = 0.5ⁿ
where , n : no. of half lives elapsed
Fraction remaining after 85% of decay = 15%
i.e., 0.15 fraction remaining.
Now, 0.5ⁿ = 0.15
= > n log 0.5 = log 0.15
= > n = log 0.15 / log 0.5
= > n = 2.7369 half lives ≈ 2.737 half lives
2.737 half lives in 1250 year then, 1 half life will long = 1250/ 2.737 years
Therefore , half-life of the isotope is = 456.704 = 4.56 x 10²
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