History Bookmarks People Window Help MasteringChemistry: Ch 13 HW htpa:/session.

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History Bookmarks People Window Help MasteringChemistry: Ch 13 HW htpa:/session.masteringchemistry.com/myct/itemView?assignmentProblemiD-59037695 106 McCoy $16 Signe 13 HWExercise 13.102 Exercise 13.102 Part A Geologists can estimate the age of rocks by their uranium-238 content. The uranium is incorporated n the rock as it hardens and then decays with first- order kinetics and a half-life of 4.5 billion years. A rock is found to contain 84.0% of the amount of uranium-238 that it contained when it was formed The amount that the rock contained when it was formed can be deduced from the presence of the decay products of U -238.) How old is the rock? Express your answer using two significant figures x® xt_ x x un x.io Submit My Answers Give Up Provid of You Get access to the latest information about paying down debt, saving for ollege, saving for retirement and starting a famlv

Explanation / Answer

Half life of Uranium-238, t1/2 = 4.5 billion years = 4.5x109 years

Amount of Uranium 238 left = 84%

rate constant, k = ln 2 / t1/2     

= 0.693 / 4.5x109 years

= 1.54x10-10 year-1

We know that, radioactive decay is a first order reaction.

N(t) = No e -t *k  

We have,

N(t) / No = 0.84

So,

N(t) / No = e -t *k  

0.84 = e -t *(1.54x10^-10)

Taking natural log on both sides:

ln 0.84 = ln [e -t *(1.54x10^-10) ]

- 0.174 = - t * (1.54x10-10 )

t = 0.174 / 1.54x10-10

t = 0.1129 x 1010 years

t = 1.13 x 109 years

or

t = 1.13 billion years

So the rock is 1.13 billion years old

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