JEE Mains · Physics · STD 12 - 13. Nuclei
What is the half-life (in years) period of a radioactive material if its activity drops to \(1 / 16^{\text {th }}\) of its initial value of \(30\) years?
- A \(9.5\)
- B \(8.5\)
- C \(7.5\)
- D \(10.5\)
Answer & Solution
Correct Answer
(C) \(7.5\)
Step-by-step Solution
Detailed explanation
\(A=A_{0} e^{-\lambda t}\) \(-\lambda t =\ln \left(\frac{ A }{ A _{0}}\right)\) \(-\frac{\ln 2}{ t _{1 / 2}} \times 30=\ln \left(\frac{1}{16}\right)\) \(-\frac{\ln 2}{t_{1 / 2}} \times 30=-4 \ln 2\) \(t _{1 / 2}=\frac{30}{4}=7.5\,yrs\)
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