Answer:
25 years.
Step-by-step explanation:
From the question given above, the following data were obtained:
Original amount (N₀) = 10 g
Time (t) = 50 years
Amount remaining (N) = 2.5 g
Half-life (t½) =?
Next, we shall determine the number of half-lives that has elapse. This can be obtained as follow:
Original amount (N₀) = 10 g
Amount remaining (N) = 2.5 g
Number of half-lives (n) =?
N = 1/2ⁿ × N₀
2.5 = 1/2ⁿ × 10
Cross multiply
2.5 × 2ⁿ = 10
Divide both side by 2.5
2ⁿ = 10 / 2.5
2ⁿ = 4
Express 4 in index form with 2 as the base.
2ⁿ = 2²
n =2
Thus, 2 half-lives has elapsed.
Finally, we shall determine the half-life of the radioactive substance. This can be obtained as follow:
Time (t) = 50 years
Number of half-lives (n) = 2
Half-life (t½) =?
n = t / t½
2 = 50 / t½
Cross multiply
2 × t½ = 50
Divide both side by 2
t½ = 50 / 2
t½ = 25 years.
Thus, the half-life of the radioactive substance is 25 years.