. S-35 (t1/2 = 87.4 d) is used in cancer research. The biological half-life in the human body is 90 days. What is the effective half-life of S-35?
To calculate the effective half-life of S-35, we need to consider both the physical half-life (t1/2) and the biological half-life.
The physical half-life is given as 87.4 days, which means that after 87.4 days, half of the original amount of S-35 will have decayed.
The biological half-life is given as 90 days, which means that in the human body, half of the remaining amount of S-35 will be eliminated every 90 days.
To find the effective half-life, we need to consider both the radioactive decay and the elimination in the body. We can combine these two rates using the concept of a "decay constant" (λ), which is the reciprocal of the half-life.
1. Calculate the decay constant for the physical half-life (λ_physical) using the formula:
λ_physical = ln(2) / t1/2_physical
λ_physical = ln(2) / 87.4
2. Calculate the decay constant for the biological half-life (λ_biological) using the formula:
λ_biological = ln(2) / t1/2_biological
λ_biological = ln(2) / 90
3. Calculate the effective decay constant (λ_effective) by adding the decay constants:
λ_effective = λ_physical + λ_biological
4. Calculate the effective half-life (t1/2_effective) using the formula:
t1/2_effective = ln(2) / λ_effective
Now, let's put these numbers into the formulas to calculate the effective half-life.