Answer:
73 days
Step-by-step explanation:
From the question given above, the following data were obtained:
Half life (t½) = 18.2 day.
Original amount (N₀) = 0.70 g
Amount remaining (N) = 0.04375 g
Time (t) =.?
Next, we shall determine the rate of decay of the isotope. This can be obtained as follow:
Half life (t½) = 18.2 day.
Decay constant (K) =.?
K = 0.693 / t½
K = 0.693 / 18.2
K = 0.038 /day
Finally, we shall determine the time taken for the isotope to decay to 0.04375 g. This can be obtained as follow:
Original amount (N₀) = 0.70 g
Amount remaining (N) = 0.04375 g
Decay constant (K) = 0.038 /day
Time (t) =.?
Log(N₀/N) = kt /2.303
Log (0.70/0.04375) = (0.038 × t) /2.303
Log 16 = (0.038 × t) /2.303
1.2041 = (0.038 × t) /2.303
Cross multiply
1.2041 × 2.303 = 0.038 × t
Divide both side 0.038
t = (1.2041 × 2.303) / 0.038
t = 72.97 ≈ 73 days
Therefore, it will take approximately 73 days for the isotope to decay to 0.04375 g