Answer:
60 days.
Step-by-step explanation:
Let the original mass (N₀) = 1 g
Amount remaining (N) = 6.25% of its original mass
= 6.25% × 1
= 6.25/100 × 1
= 0.0625 g
Half life (t½) = 15 days
Time (t) =?
Next, we shall determine the rate of decay. This can be obtained as follow:
Decay constant (K) = 0.693/ half life
K = 0.693 / t½
Half life (t½) = 15 days
Decay constant (K) =?
K = 0.693 / t½
K = 0.693 / 15
K = 0.0462 / day
Finally, we shall determine the time taken for the sample of the isotope to decay to 6.25% of its original mass.
This can be obtained as follow:
Original amount (N₀) = 1 g
Amount remaining (N) = 0.0625 g
Decay constant (K) = 0.0462 / day
Time (t) =?
Log (N₀/N) = Kt/2.3
Log (1/0.0625) = 0.0462 × t / 2.3
Log 16 = 0.0462 × t / 2.3
1.2041 = 0.0462 × t /2.3
Cross multiply
0.0462 × t = 1.2041 × 2.3
Divide both side by 0.0462
t = (1.2041 × 2.3)/0.0462
t = 59.9 ≈ 60 days
Therefore, the time taken for the sample of the isotope to decay to 6.25% of its original mass is 60 days