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The isotope Sr-90 is one of the extremely hazardous species in the residues from nuclear power generation. The strontium in a 0.500-g sample diminishes to 0.393 g in 10.0 y.rncalculate the half-life.rn-28.8 yrsrn0.127 yrsrn28.8 yrsrn0.0241 yrs
Accepted Answer
The half-life of Sr-90 can be calculated using the following equation:
ln(N(t)/N(0)) = -kt
where:
N(t) is the amount of Sr-90 remaining after time t
N(0) is the initial amount of Sr-90
k is the decay constant
t is the time elapsed
We are given that N(t) = 0.393 g, N(0) = 0.500 g, and t = 10.0 y. Plugging these values into the equation above, we get:
ln(0.393 g / 0.500 g) = -k(10.0 y)
Solving for k, we get:
k = 0.0241 y^-1
The half-life (t1/2) is related to the decay constant by the following equation:
t1/2 = ln(2) / k
Plugging in the value of k that we calculated, we get:
t1/2 = ln(2) / 0.0241 y^-1 = 28.8 y
Therefore, the half-life of Sr-90 is 28.8 years. The correct answer is 28.8 yrs.
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