Concept explainers
Interpretation:
The half-life of the isotope is to be calculated.
Concept introduction:
The amount of time required for the concentration of a radioactive decay to reduce to half of its original valueis known as half-life
The expression for the first order reaction is as follows:
Here,
Answer to Problem 1KSP
Solution: Option (d)
Explanation of Solution
Reason for the correct option:
Let the initial concentration
Calculate the rate constant from the expression of first order reaction as follows:
Rearrange the above equation for rate constant as follows:
Substitute 10 for
Thus,
Calculate the half-life of the isotope as follows:
Substitute
Thus,
So, the half-life of the isotope is
Hence, option (d) is correct.
Reason for the incorrect option:
Option (a) is incorrect because the calculated value of half-life of the isotope does not match with the given value in option (a).
Option (b) is incorrect because the calculated value of half-life of the isotope does not match with the given value in option (b).
Option (c) is incorrect because the calculated value of half-life of the isotope does not match with the given value in option (c).
Option (e) is incorrect because the calculated value of half-life of the isotope does not match with the given value in option (e).
Hence, options (a), (b), (c), and (e) are incorrect.
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Chapter 14 Solutions
Chemistry
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