Answer:
57 mins
Explanation:
From the question given above, the following data were obtained:
Half life (t₁/₂) = 19 mins
Original amount (N₀) = 100 g
Amount remaining (N) = 12.5 g
Time (t) =?
Next, we shall determine the number of half-lives (n) that wound have elapse for 12.5 g of the sample to remain. This can be obtained as follow:
Original amount (N₀) = 100 g
Amount remaining (N) = 12.5 g
Number of half-lives (n) =?
N = 1/2ⁿ × N₀
12.5 = 1/2ⁿ × 100
Cross multiply
12.5 × 2ⁿ = 100
Divide both side by 12.5
2ⁿ = 100 /12.5
2ⁿ = 8
Express 8 index with 2 as the base
2ⁿ = 2³
n = 3
Finally, we shall determine the time taken for 100 g of the isotope to decay to 12.5 g. This can be obtained as follow:
Half life (t₁/₂) = 19 mins
Number of half-lives (n) = 3
Time (t) =?
t = n × t₁/₂
t = 3 × 19
t = 57 mins
Thus, it will take 57 mins 100 g of the isotope to decay to 12.5 g.
