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= 176.5 h) to decay. Use the Calculate the time required for 46.80 % of a sample of X (t, formula with 0.693 instead of In 2.

= 176.5 h) to decay. Use the Calculate the time required for 46.80 % of a sample of X (t, formula with 0.693 instead of In 2.

Introductory Chemistry For Today
Introductory Chemistry For Today
8th Edition
ISBN:9781285644561
Author:Seager
Publisher:Seager
Chapter10: Radioactivity And Nuclear Processes
Section: Chapter Questions
Problem 10.19E
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Please answer in reagular notation 

86x (12 =D176.5h) to decay. Use the Calculate the time required for 46.80 % of a sample of formula with 0.693 instead of In 2.
Transcribed Image Text:86x (12 =D176.5h) to decay. Use the Calculate the time required for 46.80 % of a sample of formula with 0.693 instead of In 2.
Expert Solution
Step 1

Given : Half life i.e t1/2 of reactant (radioactive isotope) = 176.5 hr.

And percent of reactant reacted 46.80 %.

 

Step 2

Since the decay reactions are first order reactions.

And we know that the relationship between the amount of reactant i.e [A] and time for a first order reaction is given by 

=> ln[A]0[A] = Kt

where [A] = final amount of reactant = (1 - 0.4680) [A]0 = 0.532 [A]0                            (because 46.8 % is decaying)

[A]0 = initial amount of reactant = [A]0 

t = time 

K = Rate constant 

 

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