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How long will it take 70 grams of cobalt-60 to decay to 17.5 grams

How long will it take 70 grams of cobalt-60 to decay to 17.5 grams

Chemistry: Principles and Practice
Chemistry: Principles and Practice
3rd Edition
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Chapter21: Nuclear Chemistry
Section: Chapter Questions
Problem 21.41QE
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How long will it take 70 grams of cobalt-60 to decay to 17.5 grams? Half life of cobalt-60 is 5.3 years. Explain the solution and how you got there.

Expert Solution
Step 1

Given:

Initial amount=70 g

Final amount=17.5 g

Half life=5.3 years

Formula used:

t12=ln 2r

A=A0ert

Step 2

It is known that,

t12=ln 2r

where,

  • t12 represents half life

Thus the half life is given as 5.3 years

Here substituting the values in t12=ln 2r

5.3=ln 2r

On rearranging the equation for calculating the value of r

r=ln 25.3

On simplifying 

r=0.13078

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