Answer:
1/16
Explanation:
From the question given above, the following data were obtained:
Half-life (t½) = 269 years
Time (t) = 1076 years
Fraction remaining =?
Next, we shall determine the number of half-lives that has elapsed. This can be obtained as follow:
Half-life (t½) = 269 years
Time (t) = 1076 years
Number of half-lives (n) =?
n = t / t½
n = 1076 / 269
n = 4
Thus, 4 half-lives has elapsed.
Finally, we shall determine the fraction of the original amount remaining. This can be obtained as follow:
Let N₀ be the original amount.
Let N be the amount remaining.
Number of half-lives (n) = 4
Fraction remaining (N/N₀ ) =?
N = 1/2ⁿ × N₀
N = 1/2⁴ × N₀
N = 1/16 × N₀
Divide both side by N₀
N/N₀ = 1/16
Thus, the fraction of the original amount remaining is 1/16
