Answer:
1720 years is the amount of time that will pass.
Option a) 1720 years is the correct answer
Explanation:
Given the data in the question;
Number of nuclei initially N₀ = 60 million = 60,000,000
After time t, Number of nuclei remaining N = 3.75 × 10⁶
Also given that; half-life of radioactive americium = 430 years.
so;
λ = ln2 /
we substitute
λ = ln2 / 430 years
N = N₀e^(-λt)
solve for t
t = 1/λ × ln( N₀/N )
so we substitute
t = 1 / (ln2 / 430 years) × ln( 60,000,000 / ( 3.75 × 10⁶ ) )
t = ( 430 years / ln2 ) × ln( 60,000,000 / ( 3.75 × 10⁶ ) )
t = ( 430 years / 0.693147 ) × ln( 16 )
t = 620.359 years × 2.7725887
t = 1720.0003 ≈ 1720 years
Therefore, 1720 years is the amount of time that will pass.
Option a) 1720 years is the correct answer