Answer:
14 hrs.
Step-by-step explanation:
From the question given above, the following data were obtained:
Time (t) = 42 hrs
Original amount (N₀) = 4.32 g
Amount remaining (N) = 0.54 g
Half-life (t½) =…?
Next, we shall determine number of half-lives required for 4.32 g of the isotope to decay to 0.54 g. This can be obtained as follow:
Original amount (N₀) = 4.32 g
Amount remaining (N) = 0.54 g
Number of half-lives (n) =?
N = 1/2ⁿ × N₀
0.54 = 1/2ⁿ × 4.32
Cross multiply
0.54 × 2ⁿ = 4.32
Divide both side by 0.54
2ⁿ = 4.32 / 0.54
2ⁿ = 8
Express 8 in index form with 2 as the base
2ⁿ = 2³
n = 3
Thus, it took 3 half lives for 4.32 g of the isotope to decay to 0.54 g.
Finally, we shall determine the half-life of the isotope. This can be obtained as follow:
Time (t) = 42 h
Number of half-lives (n) = 3
Half-life (t½) =
n × t½ = t
3 × t½ = 42
Divide both side by 3
t½ = 42 / 3
t½ = 14 hrs
Thus, the half-life of the isotope is 14 hrs