Answer:
The decay of Th-234 follows the exponential decay model:
N(t) = N0 e^(-kt)
where
N0 = initial quantity of the substance
N(t) = quantity of the substance at time t
k = decay constant
t = time elapsed
The half-life of Th-234 is 24.1 days, which means that:
0.5N0 = N0 e^(-k*24.1)
Taking the natural logarithm of both sides gives:
ln(0.5) = -k*24.1
k = ln(0.5)/24.1
k = 0.0288 per day
After 145 days, the amount of Th-234 remaining can be calculated by:
N(145) = N0 e^(-0.0288*145)
N(145) = 576 mg * e^(-4.165)
N(145) = 576 mg * 0.0157
N(145) = 9.05 mg
Therefore, after 145 days, approximately 9.05 mg of Th-234 remains from the initial 576 mg sample.