Maths · The solution of differential equation by the method of separation of variables
A certain radioactive material is known to decay at a rate proportional to the a
A certain radioactive material is known to decay at a rate proportional to the amount present. If after one hour it is observed that 10 percent of the material has decayed, find the half-life (period of time it takes for the amount of material to decrease by half) of the material (in hrs.)
- A. 6.58
- B. 8.58
- C. 10.58
- D. 12.58
Step-by-step solution
The decay follows exponential decay: N(t) = N0 e^{-kt}. After 1 hour, 90% remains: e^{-k} = 0.9 → k = -ln(0.9). Half-life T satisfies e^{-kT} = 0.5 → T = ln2/k = ln2 / ln(10/9) ≈ 0.6931 / 0.1054 ≈ 6.58 hours.
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