Answer:
12.5 g
Step-by-step explanation:
From the question given above, the following data were obtained:
Half-life (t½) = 432 years.
Original amount (N₀) = 100 g
Time (t) = 1296 years
Amount remaining (N) =?
Next, we shall determine the number of half-lives that has elapse. This can be obtained as follow:
Half-life (t½) = 432 years.
Time (t) = 1296 years
Number of half-lives (n) =?
n = t / t½
n = 1296 / 432
n = 3
Thus, 3 half-lives has elapsed.
Finally, we shall determine the amount of the isotope remaining. This can be obtained as follow:
Original amount (N₀) = 100 g
Number of half-lives (n) = 3
Amount remaining (N) =?
N = 1/2ⁿ × N₀
N = 1/2³ × 100
N = 1/8 × 100
N = 0.125 × 100
N = 12.5 g
Thus, 12.5 g of the isotope is remaining.