Concept explainers
The half-life of isotope X.
Answer to Problem 75AP
The half-life of isotope X is
Explanation of Solution
Write the relation connecting the initial amount of the isotopes.
Here,
Write the relation connecting the amount of the isotopes after 3 days.
Here,
Write the equation for the amount of isotope left after 3 days.
Here,
Write the equation for decay constant.
Here,
Conclusion:
Rewrite equation (II) using equation (III).
Here,
Substitute equation (I) in the above equation and rearrange to find
Take natural logarithm on both sides and substitute equation (IV) to find
Here,
Substitute
Thus, the half-life of isotope X is
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Chapter 44 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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