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Sir, please solve: At a certain instant, a piece of radioactive material contains 10 12 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 10 4 atoms remain? (iii) What is the count rate after this time?

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?

Grade:12

2 Answers

Abhishek Kumar
askIITians Faculty 255 Points
9 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
Fareena
13 Points
3 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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