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Grade 12Modern Physics

Sir, please solve:
At a certain instant, a piece of radioactive material contains 1012 atoms. The half-life of the material is 30 days.
(i) Find the number of disintegrations in the first second.
(ii) What time would elapse before 104 atoms remain?
(iii) What is the count rate after this time?

Profile image of Utkarsh Shukla
11 Years agoGrade 12
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2 Answers

Profile image of Abhishek Kumar
11 Years ago
half life = 1/\lambda
so, \lambda = 1/(30 X24 X 60 X 60)
So, 1) dN = \lambda x 1012 x1 (\lambdaNdt)
2) If N = 104 = 1012 e-\lambdat
Solve for t, rest things are known.
3) Count rate = \lambdaN = \lambda104
Profile image of Fareena
5 Years ago
1) lambda= 0.693/t(1/2)
     lambda = 0.693/30       t(1/2)=30 days (given)
     lambda = 0.0231/day
     -dN/dt= N lambda
                = 10^12 × 0.0231
                = 2.31 × 10^10 disintegration/day
                = 2.31×10^10 ÷ 24×3600
                = 2.7× 10^5 disintegration/second

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