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JIPMER 2011
Exam
JIPMER
Year
2011
Subject
Physics
Chapter
Nuclear Physics

JIPMER 2011 · Physics · Nuclear Physics

Activity of a radioactive sample decreases to (1/3)rd of its...

Activity of a radioactive sample decreases to (1/3)rd of its original value in 3 days. Then, in 9 days its activity will become

Options

  1. A(1/27)(1 / 27) of the original value
  2. B(1/9)(1 / 9) of the original value
  3. C(1/18)(1 / 18) of the original value
  4. D(1/3)(1 / 3) of the original value

Correct answer

A. (1/27)(1 / 27) of the original value

Step-by-step solution

R=R0e−λtR=R_0 e^{-\lambda t} ⇒(13)=e−λ×3=e−3λ\Rightarrow \quad\left(\frac{1}{3}\right)=e^{-\lambda \times 3}=e^{-3 \lambda} ...(i) Again, R′R0=e−λ×9=e−9λ=(e−3λ)3\frac{R^{\prime}}{R_0}=e^{-\lambda \times 9}=e^{-9 \lambda}=\left(e^{-3 \lambda}\right)^3 =(13)3=\left(\frac{1}{3}\right)^3 [From Eq. (i)] =127=\frac{1}{27} ∴R′=R027\therefore \quad R^{\prime}=\frac{R_0}{27} Hence, in 9 days activity will become (127)\left(\frac{1}{27}\right) of the original value.
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