
Concept explainers
(a)
Interpretation:
The amount of each isotope present after 8.0 days needs to be determined.
Concept Introduction:
Half-life − It is the time required by original radioactive element to reduce to the half of its initial concentration. Thus, at half-life (
The decay of the radioactive element can be described by the following formula-
Where
N(t) − amount of reactant at time t
N0 − Initial concentration of the reactant
t1/2 − Half-life of the decaying reactant

Answer to Problem 51P
After 8.0 days,
Amount of Iodine-131 left = 32 mg
Amount of Xenon-131 formed = 32 mg
Explanation of Solution
Given Information:
N0 = 64 mg
t1/2 = 8 days
Calculation:
After 8.0 days, the initial concentration of Iodine -131 reduces to half of its initial concentration and converts to Xenon-131.
Thus,
Hence,
Amount of Iodine-131 left = 32 mg
Amount of Xenon-131 formed = 64 mg − 32 mg = 32 mg
(b)
Interpretation:
The amount of each isotope present after 16 days needs to be determined.
Concept Introduction:
Half-life − It is the time required by original radioactive element to reduce to the half of its initial concentration. Thus, at half-life (
The decay of the radioactive element can be described by the following formula-
Where
N(t) − amount of reactant at time t
N0 − Initial concentration of the reactant
t1/2 − Half-life of the decaying reactant

Answer to Problem 51P
After 16.0 days,
Amount of Iodine-131 left = 16 mg
Amount of Xenon-131 formed = 48 mg
Explanation of Solution
Given Information:
N0 = 64 mg
t1/2 = 8 days
t = 16.0 daysCalculation:
After 16 days, amount of iodine-131 would be defined by N(t),where t is 16.0 days, as
Hence, the amount of Iodine-131 decays and converts to Xenon. Therefore,
Amount of Iodine-131 left after 16.0 days = 16 mg
Amount of Xenon-131 formed after 16.0 days = 64 mg − 16mg = 48 mg
(c)
Interpretation:
The amount of each isotope present after 24 days needs to be determined.
Concept Introduction:
Half-life − It is the time required by original radioactive element to reduce to the half of its initial concentration. Thus, at half-life (
The decay of the radioactive element can be described by the following formula-
Where
N(t) − amount of reactant at time t
N0 − Initial concentration of the reactant
t1/2 − Half-life of the decaying reactant

Answer to Problem 51P
After 24.0 days,
Amount of Iodine-131 left = 8 mg
Amount of Xenon-131 formed = 56 mg
Explanation of Solution
Given Information:
N0 = 64 mg
t1/2 = 8 days
t = 24.0 days
Calculation:
After 24.0 days, amount of iodine-131 would be defined by N(t),where t is 24.0 days, as
Hence, the amount of Iodine-131 decays and converts to Xenon. Therefore,
Amount of Iodine-131 left after 24.0 days = 8 mg
Amount of Xenon-131 formed after 24.0 days = 64 mg − 8 mg = 56 mg
(d)
Interpretation:
The amount of each isotope present after 32 days needs to be determined.
Concept Introduction:
Half-life − It is the time required by original radioactive element to reduce to the half of its initial concentration. Thus, at half-life (
The decay of the radioactive element can be described by the following formula-
Where
N(t) − amount of reactant at time t
N0 − Initial concentration of the reactant
t1/2 − Half-life of the decaying reactant

Answer to Problem 51P
After 32.0 days,
Amount of Iodine-131 left = 4 mg
Amount of Xenon-131 formed = 60 mg
Explanation of Solution
Given Information:
N0 = 64 mg
t1/2 = 8 days
t = 32.0 days
Calculation:
After 32 days, amount of iodine-131 would be defined by N(t),where t is 32.0 days, as
Hence, the amount of Iodine-131 decays and converts to Xenon. Therefore,
Amount of Iodine-131 left after 32.0 days = 4 mg
Amount of Xenon-131 formed after 32.0 days = 64 mg − 4 mg = 60 mg
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Chapter 10 Solutions
General, Organic, and Biological Chemistry - 4th edition
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