JEE Mains · Physics · STD 12 - 13. Nuclei
The nuclear activity of a radioactive element becomes \(\left(\frac{1}{8}\right)^{\text {th }}\) of its initial value in \(30\, years.\) The half-life of radioactive element is \(....\,years.\)
- A \(15\)
- B \(10\)
- C \(20\)
- D \(25\)
Answer & Solution
Correct Answer
(B) \(10\)
Step-by-step Solution
Detailed explanation
\(A = A _{0} e ^{-\lambda t }\) \(\frac{ A _{0}}{8}= A _{0} e ^{-\lambda t } \Rightarrow \lambda t =\ln 8\) \(\lambda t =3 \ln 2\) \(\frac{\ln 2}{\lambda}=\frac{ t }{3}=\frac{30}{3}\) \(10\;years\)
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