Answer:
Option C. 2 half lives.
Explanation:
The following data were obtained from the question:
Original amount (N₀) = 1000 atoms
Amount remaining (N) = 250 atoms
Number of half-lives (n) =?
Half-life is defined as the time taken for the substance to reduce to half its original side. Mathematically, it can be obtained as follow:
N = 1/2ⁿ × N₀
N is the amount remaining.
n is the number of half-lives.
N₀ is the original amount.
Using the above formula, we can obtain the number of half-lives as follow:
Original amount (N₀) = 1000 atoms
Amount remaining (N) = 250 atoms
Number of half-lives (n) =?
N = 1/2ⁿ × N₀
250 = 1/2ⁿ × 1000
Cross multiply
250 × 2ⁿ = 1000
Divide both side by 250
2ⁿ = 1000/250
2ⁿ = 4
Express 4 in index form
2ⁿ = 2²
n = 2
Therefore, it will take two (2) half lives for the amount to get to 250 atoms.
