Concept explainers
The formula for the half-life can be expressed as
Want to see the full answer?
Check out a sample textbook solutionChapter 10 Solutions
Modified Mastering Physics with Pearson eText -- Standalone Access Card -- for Conceptual Integrated Science
Additional Science Textbook Solutions
University Physics Volume 2
University Physics with Modern Physics (14th Edition)
College Physics: A Strategic Approach (3rd Edition)
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Physics for Scientists and Engineers with Modern Physics
Life in the Universe (4th Edition)
- An accident at a nuclear power plant has left the surrounding area polluted with radioactive material that decays naturally. The initial amount of radioactive material present is 42 su (safe units), and 5 months later it is still 31 su. a.) write a formula giving the amount A(t) of radioactive material (in su) remaining after t months. (Use integers or decimals for any numbers in the expression. Round to three decimal places needed.) b.) what amount of radioactive material will remain after 11 months? c.) how long will it be until A = 1 su, so it is safe for people to return to the area?arrow_forwardA sample contains 1,174 nuclei of a radioactive isotope of chromium. If the half-life is 33 days, how many of the radioactive nuclei were present one year earlier? (This year lasted 365 days.) Give your answer to 3 significant figures in scientific notation (e.g. 3.29E6)arrow_forwardThe half life for the decay of carbon-14 is 5.73*10^3 years. Suppose the activity due to the radioactive decay of the carbon-14 in a tiny sample of an artifact made of wood from an archeological dig is measured to be 65. Bq. The activity in a similar-sized sample of fresh wood is measured to be 72. Bq. Calculate the age of the artifact. Round your answer to 2 significant digitsarrow_forward
- RADIOACTIVITY. LAW OF RADIOACTIVE DECAY Activity units: 1 Ci = 3.7 × 101º Bq 1. Nuclear decay law: N = Noe¬at, The law of radioactive decay gives the quantitative relationship between the original number of nuclei present at time zero No and the number N at a later time t (sec), where e = 2.71828... is the base of the natural logarithm, and 2 is the decay constant for the nuclide (1/s). 2. Relationship between decay constant 2 and isotop half-life T1/2: In(2) 0.693 Radioisotope Half-life Modality T1/2 T1/2 Carbon-11 20 minutes PET where a is decay constant (1/s), T1/2 is isotope half- life (s). 3. Activity or decay rate of a radioactive source A: ΔΝ Fluorine-18 110 minutes PET Copper-64 12.7 hours PET Gallium-67 78.3 hours SPECT Gallium-68 68 minutes PET = AN Technetum-99m 6.02 hours SPECT Δt where A is activity or decay rate of a radioactive source (Bq), N is number of nuclei present at time t (s ), 1 is decay constant (1/s). 4. Activity A of a radioactive source at a time t:…arrow_forwardRADIOACTIVITY. LAW OF RADIOACTIVE DECAY Activity units: 1 Ci = 3.7 × 1010 Bq 1. Nuclear decay law: N = Noe¬at, The law of radioactive decay gives the quantitative relationship between the original number of nuclei present at time zero No and the number N at a later time t (sec), where e = 2.71828... is the base of the natural logarithm, and 2 is the decay constant for the nuclide (1/s). 2. Relationship between decay constant 1 and isotop half-life T1/2: 0.693 T1/2 1= In(2) Half-life Modality Radioisotope T1/2 where a is decay constant (1/s), T1/2 is isotope half- life (s). Carbon-11 20 minutes PET Fluorine-18 110 minutes PET Copper-64 | 12.7 hours PET 3. Activity or decay rate of a radioactive source A: Gallium-67 AN A = At where A is activity or decay rate of a radioactive lodine-123 source (Bq), N is number of nuclei present at time t Thallium-201 (s ), 2 is decay constant (1/s). 78.3 hours SPECT | 68 minutes Gallium-68 Technetum-99m PET 6.02 hours SPECT Indium-111 | 67.3 hours SPECT…arrow_forwardA radioactive material is disintegrating in such a way that after 24 seconds, there is only 20.5% of it left. What is the half-life of the radioactive material? Express your answer in seconds and keep three significant digits. Answer:arrow_forward
- A certain radioactive material decays exponentially. The percent, P, of the material left after t years is given by P(t) = 100(1.2). a. Determine the half-life of the substance. b. How fast is the substance decaying at the point where the half-life is reached? The substance is decaying at a rate of about -3.8% per year at the time 9.12 years where the half-life is reached The substance is decaying at a rate of about -9.12% per year at the time 6.8 years where the half-life is reached The substance is decaying at a rate of about -9.12% per year at the time 3.8 years where the half-life is reached | None of the abovearrow_forwardThe radioactive gas krypton-85, produced by nuclear power plants as well as volcanoes, is present in trace amounts in earth’s atmosphere. Its half-life is 10.8 years. Suppose a volcano released 250 g of krypton-85 in an eruption. How much would remain after (a) 10.8 years, (b) 15 years, and (c) 50 years? Round to the nearest tenth of a gram.arrow_forwardLearning Goal: Radioactive decay - Half-life N 1,000,000 500,000 250,000 125,000 62,500 Number of nuclides, N x 10³ 1000 750 500 250 125 0 Time 0 the 2012 3h2 4112 5h2 612 7h2 8h2 9412 10₁2 31,250 15,625 he 2h 3h 4h 5h 6h 7he 8he 9h 10h Time in multiples of f 7,813 3,906 1,953 977 A radioactive sample's half-life is 30.2 years. 1 year = 365 days, 1 day = 24 hours, 1 hour = 60 min, 1 min = 60 sarrow_forward
- There was a sample of 500 milligrams of a radioactive substance to start a study. Since then, the sample has decayed by 2.6% each year. Let & be the number of years since the start of the study. Let y be the mass of the sample in milligrams. Write an exponential function showing the relationship between y and t.arrow_forwardThis exercise uses the radioactive decay model. The half-life of radium-226 is 1600 years. Suppose we have a 29-mg sample. (a) Find a function m(t) = mo2-t/h that models the mass remaining after t years. m(t) 1600 29 2 (b) Find a function m(t) = moe-rt that models the mass remaining after t years. (Round your r value to six decimal places m(t) = %3D (c) How much of the sample will remain after 5000 years? (Round your answer to one decimal place.) 1 mg (d) After how many years will only 17 mg of the sample remain? (Round your answer to one decimal place.) X yrarrow_forwardProblem 9: Answer the following questions based on the graph of a radioactive iodine isotope shown to the right. Part (a) What is the half-life of the material in days? t = _________ days Part (b) In how many days does the substance decay to one-fourth its original value? t = _________ daysarrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningGlencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-HillCollege PhysicsPhysicsISBN:9781285737027Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning