Chapter 15 HW Item 17 C17 of 32 ?PartA Constants I Periodic Table The half-life

Question

Chapter 15 HW Item 17 C17 of 32 ?PartA Constants I Periodic Table The half-life for the radioactive decay of U -238 pnsalolh ors and independent of nitl How long wil it take for 20% of the U-238 atoms in a sample of U-238 to decay? Express your answer using two significant figures yr Submit Previous Answers Reavest Answer Incorrect: Try Again; 8 attempts remaining Part B If a sample of U 238 initially contained 1.9*1018 atoms when the universe was formed 13.8 billion years ago, how many U-238 atoms will it contain today? Express your answer using two significant figures atoms Submit

Explanation / Answer

A.

k = 0.693 / half life time

k = 0.693 / 4.5

k = 0.154 billionyears-1

First order rate constant equation is,

k = ( 1 / t ) * ln[inital] / [Final]

0.154 = ( 1 / t ) * ln( 100 / 80 )

t = 1.54 billion years

t = 1.54 109 years

B.

0.154 = ( 1 / 13.8 ) * ln(1.9 * 1014 / N )

ln(1.9*1014 / N) = 2.125

1.9 * 1014 / N = 8.37

N = 2.27 * 1013 atoms

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