Answer:
42.9 h
Step-by-step explanation:
From the question given above, the following data were obtained:
Original amount (N₀) = 100%
Amount remaining (N) = 25%
Time (t) = 85.8 h
Half-life (t½) =?
Next, we shall determine the number of half-lives that has elapse. This can be obtained as follow:
Original amount (N₀) = 100%
Amount remaining (N) = 25%
Number of half-lives (n) =?
N = 1/2ⁿ × N₀
25 = 1/2ⁿ × 100
Cross multiply
25 × 2ⁿ = 100
Divide both side by 25
2ⁿ = 100/25
2ⁿ = 4
Express 4 index form with 2 as the base
2ⁿ = 2²
n = 2
Thus, two half-lives has elapsed.
Finally, we shall determine the half-life of the of the isotope. This can be obtained as follow:
Time (t) = 85.8 h
Number of half-lives (n) = 2
Half-life (t½) =?
n = t / t½
2 = 85.8 / t½
Cross multiply
2 × t½ = 85.8
Divide both side by 2
t½ = 85.8 / 2
t½ = 42.9 h
Thus, the half-life of the of the isotope is 42.9 h