
Concept explainers
Interpretation:
The amount, activity and the probability of
Concept introduction:
The half-life of the reaction is the period of time required for the concentration of a reactant to decrease to one-half of its initial value. It is written as t1/2. Thus, the half-life of a reaction is the time required for the reactant concentration to decrease from [N]0 to [N]0/2.
The amount of a particular radioactive isotope left after time t is given as:
Here,
is the rate constant for the radioactive decay,
Nearly all radioactive decays are of first order and the rate constant is given as:
Here,
is the half -life of the radioactive substance.
The rate of decay for a particular isotope is given by the rate law as:
Here,
is the rate constant for the radioactive decay and

Answer to Problem 88AP
Solution:
Probability is
Explanation of Solution
a) Number of
nuclei left after 30 min.
Half -life of
Initial amount of
nuclei
Time (t)
It is also known that the rate constant for the radioactive decay is given as follows:
Substitute the value of half-life in the above expression, we get rate constant,
Now, the number of Mg present after
is calculated by the expression as follows:
Here,
is the final rate of disintegration or the amount of radioactive substance left after time t.
Substitute the values of
On solving further,
Thus, the number of
is
b) The
At first, convert the rate constant unit into
It is known that one minute is equal to
Thus, the conversion factor is
The above conversion factor of the rate constant can be written as follows:
Now, at
The activity of
Substitute the values of
Now, by the definition of 1 curie,
disintegration occurs per second.
Thus, the conversion factor is
Hence, by using the above conversion factor, the rate can be converted to curie as follows:
Thus, the radioactivity of
at
is
Similarly, at
The activity of
Substitute the values
Now, by the definition of 1 curie,
disintegration occurs per second.
Thus, the conversion factor is
Hence, by using the above conversion factor, the rate can be converted to curie as:
Thus, the radioactivity of
at
is
c) The probability that
From part (b) results, it is known that the rate constant of
is
Thus, it can be said that
are occurring per second.
Hence, the probability of
that decays in
Want to see more full solutions like this?
Chapter 20 Solutions
CHEMISTRY >CUSTOM<
- For each reaction below, decide if the first stable organic product that forms in solution will create a new CC bond, and check the appropriate box. Next, for each reaction to which you answered "Yes" to in the table, draw this product in the drawing area below. Note for advanced students: for this problem, don't worry if you think this product will continue to react under the current conditions - just focus on the first stable product you expect to form in solution. དྲ。 ✗MgBr ? O CI Will the first product that forms in this reaction create a new C-C bond? Yes No • ? Will the first product that forms in this reaction create a new CC bond? Yes No × : ☐ Xarrow_forwardPredict the major products of this organic reaction: OH NaBH4 H ? CH3OH Note: be sure you use dash and wedge bonds when necessary, for example to distinguish between major products with different stereochemistry. Click and drag to start drawing a structure. ☐ : Sarrow_forwardPredict the major products of this organic reaction: 1. LIAIHA 2. H₂O ? Note: be sure you use dash and wedge bonds when necessary, for example to distinguish between major products with different stereochemistry. Click and drag to start drawing a structure. X : ☐arrow_forward
- For each reaction below, decide if the first stable organic product that forms in solution will create a new C - C bond, and check the appropriate box. Next, for each reaction to which you answered "Yes" to in the table, draw this product in the drawing area below. Note for advanced students: for this problem, don't worry if you think this product will continue to react under the current conditions - just focus on the first stable product you expect to form in solution. NH2 tu ? ? OH Will the first product that forms in this reaction create a new CC bond? Yes No Will the first product that forms in this reaction create a new CC bond? Yes No C $ ©arrow_forwardAs the lead product manager at OrganometALEKS Industries, you are trying to decide if the following reaction will make a molecule with a new C-C bond as its major product: 1. MgCl ? 2. H₂O* If this reaction will work, draw the major organic product or products you would expect in the drawing area below. If there's more than one major product, you can draw them in any arrangement you like. Be sure you use wedge and dash bonds if necessary, for example to distinguish between major products with different stereochemistry. If the major products of this reaction won't have a new CC bond, just check the box under the drawing area and leave it blank. Click and drag to start drawing a structure. This reaction will not make a product with a new CC bond. G marrow_forwardIncluding activity coefficients, find [Hg22+] in saturated Hg2Br2 in 0.00100 M NH4 Ksp Hg2Br2 = 5.6×10-23.arrow_forward
- give example for the following(by equation) a. Converting a water insoluble compound to a soluble one. b. Diazotization reaction form diazonium salt c. coupling reaction of a diazonium salt d. indacator properties of MO e. Diazotization ( diazonium salt of bromobenzene)arrow_forward2-Propanone and ethyllithium are mixed and subsequently acid hydrolyzed. Draw and name the structures of the products.arrow_forward(Methanesulfinyl)methane is reacted with NaH, and then with acetophenone. Draw and name the structures of the products.arrow_forward
- 3-Oxo-butanenitrile and (E)-2-butenal are mixed with sodium ethoxide in ethanol. Draw and name the structures of the products.arrow_forwardWhat is the reason of the following(use equations if possible) a.) In MO preperation through diazotization: Addition of sodium nitrite in acidfied solution in order to form diazonium salt b.) in MO experiment: addition of sodium hydroxide solution in the last step to isolate the product MO. What is the color of MO at low pH c.) In MO experiment: addition of sodium hydroxide solution in the last step to isolate the product MO. What is the color of MO at pH 4.5 d.) Avoiding not cooling down the reaction mixture when preparing the diazonium salt e.) Cbvcarrow_forwardA 0.552-g sample of an unknown acid was dissolved in water to a total volume of 20.0 mL. This sample was titrated with 0.1103 M KOH. The equivalence point occurred at 29.42 mL base added. The pH of the solution at 10.0 mL base added was 3.72. Determine the molar mass of the acid. Determine the Ka of the acid.arrow_forward
- Chemistry: The Molecular ScienceChemistryISBN:9781285199047Author:John W. Moore, Conrad L. StanitskiPublisher:Cengage LearningPrinciples of Modern ChemistryChemistryISBN:9781305079113Author:David W. Oxtoby, H. Pat Gillis, Laurie J. ButlerPublisher:Cengage LearningChemistry & Chemical ReactivityChemistryISBN:9781337399074Author:John C. Kotz, Paul M. Treichel, John Townsend, David TreichelPublisher:Cengage Learning
- ChemistryChemistryISBN:9781305957404Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCostePublisher:Cengage LearningChemistry: An Atoms First ApproachChemistryISBN:9781305079243Author:Steven S. Zumdahl, Susan A. ZumdahlPublisher:Cengage Learning





