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The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 95% of the lead to decay? (Round your answer to two decimal places.)

The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 95% of the lead to decay? (Round your answer to two decimal places.)

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Chemistry
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ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 95% of the lead to decay? (Round your answer to two decimal places.)
Transcribed Image Text:The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 95% of the lead to decay? (Round your answer to two decimal places.)
Expert Solution
Step 1

As radioactive decay is a first order process, 

Rate of radioactive decay, r = k [N]1 

So, integrated rate law equation is ln ([N]t/[N]o) = -λt 

[N]o is the initial number of nuclides present at time 0 = 1 g [100 %]

After decay of 95 % of Lead isotope, only 5 % of nuclides will be present 

[N]t is the number of nuclides present at time t = 0.05 [ 5 % = 5/100] 

half-life, t1/2 = 3.3 hrs

 

 

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