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NEET 2010
Exam
NEET
Year
2010
Subject
Physics
Chapter
Nuclear Physics

NEET 2010 · Physics · Nuclear Physics

The decay constant of a radio isotope is λ . If A_1 and A_2 are its...

The decay constant of a radio isotope is λ\lambda. If A_1 and A2\mathrm{A}_2 are its activities at times t1\mathrm{t}_1 and t2\mathrm{t}_2 respectively, the number of nuclei which have decayed during the time (t1−t2)\left(\mathrm{t}_1-\mathrm{t}_2\right)

Options

  1. AA1t1−A2t2\mathrm{A}_1 \mathrm{t}_1-\mathrm{A}_2 \mathrm{t}_2
  2. BA1−A2A_1-A_2
  3. C\frac{\left(A_1-A_2\right)}{\lambda}
  4. Dλ(A1−A2)\lambda\left(A_1-A_2\right)

Correct answer

C. \frac{\left(A_1-A_2\right)}{\lambda}

Step-by-step solution

A1=λN1A2=λN2N1−N2=[A1−A2λ]\begin{aligned}\mathrm{A}_{1} & =\lambda \mathrm{N}_{1} \\ \mathrm{ A}_{2} & =\lambda \mathrm{N}_{2} \\ \mathrm{ N}_{1}- \mathrm{N}_{2} & =\left[\frac{\mathrm{A}_1-\mathrm{A}_2}{\lambda}\right] \end{aligned}$$
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