Answer:
0.11 mg
Step-by-step explanation:
From the question given above, the following were obtained:
Half life (t½) = 28.8 years
Original amount ((N₀) = 2.90 mg
Time (t) = 137 years
Amount remaining (N) =?
Next, we shall determine the rate of disintegration (K). This can be obtained as follow:
Rate of decay (K) = 0.693/ half life (t½)
K = 0.693 / t½
Half life (t½) = 28.8 years
Rate of decay (K) =?
K = 0.693 / t½
K = 0.693 / 28.8
K = 0.0241 /year
Finally, we shall determine amount remaining after 137 years as follow:
Original amount ((N₀) = 2.90 mg
Time (t) = 137 years
Rate of decay (K) = 0.0241 /year
Amount remaining (N) =?
Log (N₀/N) = kt/2.3
Log (2.9/N) = 0.0241 × 137 / 2.3
Log (2.9/N) = 3.3017 / 2.3
Log (2.9/N) = 1.4355
Take the antilog of 1.4355
2.9/N = antilog (1.4355)
2.9/N = 27.26
Cross multiply
2.9 = N × 27.26
Divide both side by 27.26
N = 2.9/27.26
N = 0.11 mg
Therefore, the amount remaining after 137 years is 0.11 mg