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JEE Previous Year Question

$The nuclear activity of a radioactive element becomes (\frac{1}{8})^{th} of its initial value in 30 years. The half-life of radioactive element is years.$

Topic: JEE PYQ

Answer: 10. Full step-by-step solution below.

Correct answer: 10

Solution

(10) A = A_{0} e^{- λ . t} \frac{A _{0}}{8} = A_{0} e^{- λt} \Rightarrow λt = ln 8 λt = 3 ln 2 \frac{ln 2}{λ} = \frac{t}{3} = \frac{30}{3} = 10 years

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