Answer:
31.92 h
Explanation:
We'll begin by calculating the number of half-lives that has elapsed. This can be obtained as follow:
Original amount (N₀) = 1
Amount remaining (N) = ⅛
Number of half-lives (n) =?
N = 1/2ⁿ × N₀
⅛ = 1/2ⁿ × 1
Cross multiply
2ⁿ = 8
Express 8 in index form with 2 as the base.
2ⁿ = 2³
n = 3
Thus, 3 half-lives has elapsed.
Finally, we shall determine the time. This can be obtained as follow:
Half-life (t½) = 10.64 h
Number of half-lives (n) = 3
Time (t) =?
n = t / t½
3 = t / 10.64
Cross multiply
t = 3 × 10.64
t = 31.92 h
Therefore, it will take 31.92 h for lead-212 to decay to one-eighth its original strength.
