At a given time, t_0, sample A contains 750,000 radioactive nuclei. During the 1

Question

At a given time, t_0, sample A contains 750,000 radioactive nuclei. During the 1 hour before t_0, a total of 280,000 decays were observed from this sample.

A. Calculate the half-life of the radioactive material in Sample A.

B. Calculate the decay rate of Sample A at t_0.



The radioactive material in sample B has twice the half life of the material in sample A (found in part A), and at t_0, it has one-tenth the number of radioactive nuclei as sample A.

C. Determine the amount of time after t_0 when both samples have the same number of radioactive nuclei.

Explanation / Answer

N is the no of nuclei before 1 hour No is no. of nuclei at t= to in 1 hour 280000 decays N- No = 280000 N- Ne^(-kt) = 280000 N(1-e^(-kt) ) = 280000 put N = No/e^(-kt) No((1/e^(-kt) ) - 1) = 280000 Put value of No and t = 1 1+(28/75) = e^(k) take ln both sides k = 0.31724 i) half life = 0.693/k = 2.184 hours ii) |dN/dt| at t= 1 hours the point for to k No e^(-kt) 0.31724*750000*e^(-k) = 173250.15 per hour

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