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ChemistryIntroductory Chemistry: A Foundation9th Edition

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Chapter 19, Problem 41QAP
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Introductory Chemistry: A Foundati...

9th Edition
Steven S. Zumdahl + 1 other
ISBN: 9781337399425

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Introductory Chemistry: A Foundati...

9th Edition
Steven S. Zumdahl + 1 other
ISBN: 9781337399425
Textbook Problem
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. The element krypton has several radioactive isotopes. Below are listed several of these isotopes along with their half-lives. Which of the isotopes is most stable? Which of the isotopes is “hottest”? If we were to begin a half-life experiment with separate 125- μ g samples of each isotope,approximatelyhow much of each isotope would remain after 24 hours?

    Isotope Half-life
    Kr-73
    		 27 s
    Kr-74
    		 11.5 mm
    Kr-76
    		 14.8 h
    Kr-81
    		 2.1 × 10 5 yr

Interpretation Introduction

Interpretation:

Interpret the most stable isotope and determine the hottest isotope. Interpret the amount of following isotope left after 24 hr.

Kr-73 with half life 27 s

Kr-74 with half life 11.5 min

Kr-76 with half life 14.8 h

Kr-81 with half life 2.1 × 105yr.

Concept Introduction:

The time elapsed can be identified through the below formula:

 (N /N0) = (1 /2)t /t half

N is number of mole left after time t

N0 is initial number of mole

Th a l f is half life.

Explanation

Higher the half life, more the molecule take time to reduce to half of its concentration and is more stable that’s why it is taking more time to reduce.

Half life of Kr-81 is greatest of all that is 2.1 × 105yr and thus is more stable.

Hottest isotope have lower half life and react or disintegrate easily because of low stablity. Half life of Kr-73 is lowest of all that is 27 s and thus is less stable.

 (N /N0) = (1 /2)t /t half

Calculate N for each isotope

N 0 for each isotope = 125 micro gram

T half is given

T = 24 hr

For Kr-73

Thalf= 27 st = 24 h = 24 × 3600 = 86400 sec.N0= 125 µgN /No= ( 1/2)t / t halfN /125 = (1 /2)86400 /27N = 125 (1 /2)3200 N = 8.36 × 10-14µg

For Kr-74

Thalf= 27 st = 11.5 min = 11.5 × 60 = 690 sec.N0= 125 µgN /No= ( 1/2)t / t halfN /125 = (1 /2)690 /27N = 125 (1 /2)25

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