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JEE Advanced 2011Paper 1
Exam
JEE Advanced
Year
2011
Paper
Paper 1
Subject
Physics
Chapter
Nuclear Physics

JEE Advanced 2011 · Paper 1 · Physics · Nuclear Physics

The activity of a freshly prepared radioactive sample is 10^ 10...

The activity of a freshly prepared radioactive sample is 101010^{10} disintegrations per second, whose mean life is 10−9 s10^{-9} \mathrm{~s}. The mass of an atom of this radioisotope is 10−25 kg10^{-25} \mathrm{~kg}. The mass (in mg\mathrm{mg} ) of the radioactive sample is

Correct answer

1

Step-by-step solution

Activity (−dNdt)=λN=(1tmean )×N\left(-\frac{d N}{d t}\right)=\lambda N=\left(\frac{1}{t_{\text{mean }}}\right) \times N∴N=(−dNdt)×tmean = Total number of  atoms  Mass of one atom is 10−25kg=m (say) ∴ Total mass of radioactive substance =( number of atoms) ×( mass of one atom) =(−dNdt)(tmean )(m)\begin{aligned} & \therefore \quad N=\left(-\frac{d N}{d t}\right) \times t_{\text{mean }} \\ & \quad=\text{ Total number\text{ of } atoms } \\ & \text{ Mass of one atom is } 10^{-25} \mathrm{ kg}=m \text{ (say) } \\ & \therefore \quad \text{ Total mass of radioactive substance } \\ & =(\text{ number of atoms) } \\ & \quad \times(\text{ mass of one atom) } \\ & =\left(-\frac{d N}{d t}\right)\left(t_{\text{mean }}\right)(m) \end{aligned}Substitutingthevalues,wegetTotalmassofradioactivesubstance=1mgSubstituting the values, we get Total mass of radioactive substance =1 \mathrm{mg} \thereforeAnsweris1.AnalysisofQuestionQuestionisverysimple.Againinmyopiniononecansolveit.Answer is 1 . Analysis of Question Question is very simple. Again in my opinion one can solve it.
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