Radioactive decay is a first-order process. Radioactive decay kinetics is described by the same mathematics as chemical reaction kinetics. In a sample where the volume does not change, the concentration of a radioactive isotope, R, is proportional to all of these quantities: the radioactivity, A, the number of radioactive particles, N, theamount of radioactive particles, n, and the mass of the radioactive isotope, m. Therefore, the ratio of any of these quantities to its initial value is equal to the ratio of any other quantity to its initial value. That is,This means that the ratio of concentrations it is the same as the ratio of masses and can be used to calculate the mass of a radioisotope after a given time, given the initial mass.Step 1Use the integrated rate law equation for a first order reaction. In this case, [R]; represents the concentration of gold-198 present at any particular time and [R], is the initial concentration.Step 2Calculate the value of the rate constant, k, using the half-life.Step 3Calculate the product of time and the rate constant, kt.Step 4Calculate the ratio of concentrations before and after time has elapsed.Step 5Solve for the mass of gold-198 remaining, Rt.Radioactive gold-198 is used in the diagnosis of liver problems. The half-life of this isotope is 2.70 days. If you begin with a 5.6-mg sample of the isotope, how much of this sample remains after 5.00 days?mg

Radioactive disintegration reactions are first order reactions. Half life of first order reaction is…

Radioactive gold-198 is used in the diagnosis of liver problems. The half-life of this isotope is 2.70 days. If you begin with a 5.6-mg sample of the isotope, how much of this sample remains after 5.00 days? mg

Radioactive gold-198 is used in the diagnosis of liver problems. The half-life of this isotope is 2.70 days. If you begin with a 5.6-mg sample of the isotope, how much of this sample remains after 5.00 days? mg

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

See similar textbooks

Related questions

Q: used to treat thyroid cancer, decays with a first-order half-life of 6.99 × 105 s. How long does it…

Q: A certain rock contains 2.57 x 1017 atoms of 40k for every 7.71 x 1016 atoms of 40 Ar. Assuming that…

A: Answer:All the radioactive reactions are first order reactions. Therefore, integrated rate law for…

Q: The rate constant for the decay of a radioactive element is 2.03 × 10⁻³ day⁻¹. What is the half-life…

Q: Calculate the half-life (in minutes) for a radioactive substance which loses 42.5% of its original…

A: After 1 hour it loses 42.5% of its original intensity, which means after 1 hour 57.5% of the…

Q: Strontium-90 is one of the radioisotopes released in the Chernobyl nuclear plant accident. The…

Q: The first-order rate constant for radioactive decay of 131^l is equal to 8.642 x 10-2 day-1. Find…

A: Given : first order reaction Tip: apply decay equation

Q: Tritium is radioactive and decays by a first order process with a half-life of 12.5 yr. If an…

Q: The radioisotope strontium-90 has a half-life of 38.1 years. If a sample contains 40 mg of Sr- 90,…

Q: Will rate fast! The half-life for the radioactive decay of U-238 is 4.5 billion years and is…

A: The objective of the question is to A) Calculate the time taken for of the decay.B) Calculate the…

Q: Consider the radioisotope 226Ra (half life 1.03 x 10^5). What is the first order rate constant for…

Q: 1. Deoxyglucose labeled with 18F is commonly used in PET scan to locate tumors. The half-life of 18F…

A: In this question, we want to determine the time for the level of 18F in the body when it's drop from…

Q: 5. Both technetium-99 and thallium-201 are used to image heart muscle in patients with suspected…

A: Given,Determine the percent of radioactivity.Radioactive decay, also known as nuclear decay or…

Q: The reaction of hydrogen peroxide (H2O2(aq)) into water and oxygen is a reaction with a rate…

A: Given: Rate constant of reaction = 4.0 × 10-8 s-1. And time passed = 1.0 × 108 s.

Q: A sample of sodium-24 chloride contains 0.050 mg of Na-24. After 20.5 h, 0.019 mg of Na-24 is left.…

A: Sodium-24 is radioactive isotope of sodium-23 All radioactive reaction are first order reaction…

Q: Consider the radioisotope ⁹³Mo (half life = 4.00 × 10³ years). What is the first order rate constant…

A: For first order reaction: Rate constant, K = 0.693/t1/2 t1/2 = Half-life

Q: The rate constant for the decay of a radioactive element is 2.44 x 10 ^-3 day^-1. What is the…

Q: A certain signal molecule S in brain tissue is degraded by two different biochemical pathways: when…

A: Given: Half-life when only path 1 is active = 6.0 s. And half-life life when the only path 2 is…

Q: 8) The half-life for the (first order) radioactive decay of "C is 5730 years. An archaeological…

A: Answer: Data given- half-life for radioactive decay of 14C is 5730 yrs. 70% of the 14C found in…

Q: Consider the radioisotope "Ca (half life = 1.03 × 105 years). What is the first order rate constant…

A: Rate constant is 6.73 x 10-6 yr-1

Q: The radioisotope phosphorus-32 is used in tracers for measuring phosphorus uptake by plants. The…

A: Radioactivity follows First order reaction. For First order reaction : t1/2 = 0.693k where, t1/2 =…

Q: certain radioactive isotope, used in a dye to detect blood clots, has a half-life of 18.25 minutes.…

A: Given that:Half-life of isotope is 18.25 minutesInitial amount of isotope is 230 mg To find: The…

Q: What is the half-life of this element in days?

A: Given :- rate constant (k) = 5.29 × 10-3 day-1 To calculate :- Half life Radioactive decay…

Q: The half-life for the first order radioactive decay of 14C is 5730 years. An archeological sample…

A: The breaking down of atomic nuclei releases the energy and matter from nuclei. This process is named…

Q: The half-life of a chemical substance is 5 days. How long does it take for 1.3 Kilograms of the…

A: For first order t = 1/K × { ln Co/Ct }

Q: normal

A: In given question half life independent of the amount of the starting substance means it is a first…

Q: Chromium-51 is a radioisotope that is used to assess the lifetime of red blood cells The half-life…

A: The initial amount of Chromium-51 (No) = 54.8 mgThe half-life period of Chromium-51 (t1/2) = 27.7…

Q: The isotope 90/38 Sr is one of the extremely hazardous species in the residues from nuclear power…

Q: A chemical exposure occurs by ingestion. The dose is absorbed very quickly into the bloodstream, so…

Q: Ibuprofen, a common over‑the‑counter analgesic, often comes in doses of 200.0 mg and is usually…

Q: A certain signal molecule S in muscle tissue is degraded by two different biochemical pathways: when…

A: The formula for half-life of parallel decay is given by Where, t1/2 combined = half life when both…

Q: strontium-8 is a readioactive maker used in scanning for bone disease including cancer that decays…

Q: Sodium pertechnetate (Tc-99m) is a radiopharmaceutical used as a diagnostic agent with a half-life…

A: Given Half life ( t1/2) for the sodium pertechnetate i.e. t1/2 = 6.01 hour The decay of sodium…

Q: The isotope Cesium 137, which has a half-life of 30 years, a product of nuclear power plants. How…

A: Here it is required to find the time needed for a radioactive isotope of cesium-137 to decay to…

Q: A given compound decomposes with a half-life of 8.0 s and the half-life is independent of the…

A: We have to calculate the time taken.

Q: The rate constant for the decay of a radioactive element is 4.18 × 10⁻³ day⁻¹. What is the half-life…

Q: The rate constant for the decay of a radioactive element is 1.95 × 10⁻³ day⁻¹. What is the half-life…

A: The objective of this question is to calculate the half-life of a radioactive element given its rate…

Q: Strontium-90 is one of the radioisotopes released in the Chernobyl nuclear plant accident. The…

Q: Scientists working in Lake Apoka calculating half-lives of pollutants called volatile organic…

A: Given that the half-life (t1/2 ) is 37.3 days and the concentration ([A]) is 0.835 M at that time.

Q: Two lakes are connected to each other as shown in the figure below. Each lake has a volume of 106 m³…

A: (i) To determine the steady-state concentrations in the effluent from the lakes, we'll need to set…

Q: Elements heavier than uranium in the periodic table do not exist in any appreciable amounts in…

A: Elements below uranium have short half lives yet they exist in nature whereas higher elements do…

Q: the half-life of radium 226 is 1620 years. how many hours will it take for a 5g sample to decay to…

A: The radioactive decay is a first order reaction. Since we know that the relationship between the…

Q: Radioactive gold 198 is used in the diagnosis of liver problems. The half-life of the isotope is…

Q: the half-life of fluorine 18 is 109.77 minutes how long will it take for a 6.250 % of the original…

A: The objective of this question is to determine the time it will take for only 6.250% of the original…

Q: gallium-67? What are the units for k?

A: Half life time(t1/2) = 78.25 hrs Aa we know Radioactive decay follows first order kinetics Rate…

Question

Radioactive decay is a first-order process. Radioactive decay kinetics is described by the same mathematics as chemical reaction kinetics. In a sample where the volume does not change, the concentration of a radioactive isotope, R, is proportional to all of these quantities: the radioactivity, A, the number of radioactive particles, N, the
amount of radioactive particles, n, and the mass of the radioactive isotope, m. Therefore, the ratio of any of these quantities to its initial value is equal to the ratio of any other quantity to its initial value. That is,
This means that the ratio of concentrations it is the same as the ratio of masses and can be used to calculate the mass of a radioisotope after a given time, given the initial mass.
Step 1
Use the integrated rate law equation for a first order reaction. In this case, [R]; represents the concentration of gold-198 present at any particular time and [R], is the initial concentration.
Step 2
Calculate the value of the rate constant, k, using the half-life.
Step 3
Calculate the product of time and the rate constant, kt.
Step 4
Calculate the ratio of concentrations before and after time has elapsed.
Step 5
Solve for the mass of gold-198 remaining, Rt.
Radioactive gold-198 is used in the diagnosis of liver problems. The half-life of this isotope is 2.70 days. If you begin with a 5.6-mg sample of the isotope, how much of this sample remains after 5.00 days?
mg

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.

Similar questions

The rate constant for the decay of a radioactive element is 6.37 × 10⁻³ day⁻¹. What is the half-life of this element in days?
If the half life of hydrogen peroxide is 949 sec and you started with 3M H2O2, how much hydrogen peroxide is left after 79 hours?
3. For the reaction 2A + 3B 4C + 5D, if the rate of the reaction in terms of AB is 6.69 x 10 Mol/L/s, what would be the rate of AD?
[References] Use the References to access important values if needed for this question. The half-life of the radioactive isotope phosphorus-32 is 14.3 days. How long will it take for the mass of a sample of phosphorus-32 to decay from 61.3 micrograms to 15.3 micrograms? days
Radioactive decay occurs following first order kinetics. If the half-life of a sample of Cl-36 is 3.0 x 105 years, what is the value of the rate constant, k in s-1? t1/2=0.693k
A certain signal molecule S in brain tissue is degraded by two different biochemical pathways: when only Path 1 is active, the half-life of S is 9.0 s. When only Path 2 is active, the half-life of S is 67.7 s. Calculate the half-life of S when both pathways are active. Rounded your answer to 2 significant digits.
Please solve
8. Determine the half-life of an anti-hypertensive'drug if it appears to be eliminated from the body at a rate constant of 46% per hour.
In a patient, the fraction of radioactive iodine 131I (Iodine) remaining after 32 days was found to be 1/16. Using this information and your knowledge of the rate law, show that the half-life of radioactive iodine is 8.0 days.
Consider the radioisotope ⁴¹Ca (half life = 1.03 × 10⁵ years). What is the first-order rate constant for ⁴¹Ca?
The rate constant for the decay of a radioactive element is 2.09 x 10 3 day1. What is the half-life of this element? days 1 4 6. 8 9. +/- x 100 12:01 AM Type here to search 4/17/2021 3. 7. 近

5. A reaction has the expeimental rate law = rate = k[A]2[B]. If the concentraion of A is doubled and the concentration of B is halved, what happens to the reaction rate? 11. Studies of radioactive decay of nuclei show that the decay rate of the radioactive sample is proportional to the amount of the radioactive species present. Once half the radioactivity has disappeared, the radioactive decay rate is only half of its original value. Is radioactive decay a zeroth-order, first order, or second order process? 13. Which of these reactions are unimolecular and elementary, which are bimolecular and elementary, and which are not elementary? a. HCl(g) + H2O(g) -----> H3O+(g) + Cl-(g) b. I- (g) + CH3Cl(g) ----> ICH3(g) + Cl-(g) c. C2H6 (g) -----> C2H4(g) + H2(g) d. N2(g) = 3 H2(g) ---> 2 NH3 (g) e. O2(g) = O(g) ---> O3(g) 15. The activation energy Ea is 139.7 kJ mol-1 for the gas pahse reaction HI + CH3I ----> CH4 + I2 Calculate the fraction of the molecules whose…