The time taken for the radioactive material to decay from 1600 counts per min to 100 counts per min is 80 minutes
We'll begin by calculating the number of half-lives that has elapsed. This can be obtained as follow:
Original amount (N₀) = 1600 count per min
Amount remaining (N) = 100 count per min
Number of half-lives (n) =?
N × 2ⁿ = N₀
100 × 2ⁿ = 1600
Divide both side by 100
2ⁿ = 1600 / 100
2ⁿ = 16
2ⁿ = 2⁴
n = 4
Thus, 4 half-lives has elapsed
Finally, we shall determine the time taken for the radioactive material to reduce to 100 counts per min. This can be obtained as follow;
Number of half-lives (n) = 4
Half-life (t½) = 20 mins
Time (t) =?
t = n × t½
t = 4 × 20
t = 80 mins
Therefore, it will take 80 mins for the radioactive material to decay to 100 counts per min
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