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First Order Half Life Solutions Library

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First Order Half Life

Q. The nuclide 96Nb decays by a first-order process with a rate constant of 2.96×10–2 min-1. How long will it take for 26.0% of the initial amount of ...

Solved • Feb 17, 2020

First Order Half Life

Q. The half-life of N2O5 (g) at a 25 °C is 4.03 x 104 s. a) Find the rate constant (k) for the first-order decomposition of N2O5 (g) at 25 °C. 

Solved • Jan 20, 2020

First Order Half Life

Q. Nuclear decay is a first-order kinetic process. Therefore, If N0 nuclei are present at time t = 0, the number remaining at time t is given by the e...

Solved • Jan 6, 2020

First Order Half Life

Q. Nuclear decay is a first-order kinetic process. Therefore, If N0 nuclei are present at time t = 0, the number remaining at time t is given by the e...

Solved • Jan 6, 2020

First Order Half Life

Q. A sample containing a radioactive isotope produces 2000 counts per minute in a Geiger counter. After 120 hours, the sample produces 250 counts per ...

Solved • Dec 20, 2019

First Order Half Life

Q. An artifact showed a carbon­-14 decay rate of 13.8 disintegrations/min per gram of carbon. Carbon-­14 has a half­-life of 5715 years, and currently...

Solved • Dec 19, 2019

First Order Half Life

Q. The half-life of cesium-130 is 15 minutes. What percentage of the initial activity will be present after 75 minutes, assuming radioactive decay occ...

Solved • Dec 19, 2019

First Order Half Life

Q. 210Pb has a half-life of 22.3 years and decays to produce 206Hg. If you start with 7.50 g of 210Pb, how many grams of 206Hg will you have after 17....

Solved • Dec 19, 2019

First Order Half Life

Q. Strontium-90 is a byproduct in nuclear reactors fueled by the radioisotope uranium-235. The of is 28.8 yr. What percentage of a strontium-90 sample...

Solved • Dec 19, 2019

First Order Half Life

Q. The half-life for beta decay of strontium-90 is 28.8 years. A milk sample is found to contain 10.3 ppm strontium-90. How many years would pass befo...

Solved • Dec 19, 2019

First Order Half Life

Q. The half-life of 222Rn is 3.80 days. If a sample contains 36.0 g of Rn-222, how many years will it take for the sample to be reduced to 1.00 mg of ...

Solved • Dec 18, 2019

First Order Half Life

Q. The half-life of carbon-14 is 5730 years. If a sample initially contains 2.67 mg carbon-14, what mass remains in the sample after 2.40 ξ 104 years?...

Solved • Dec 18, 2019

First Order Half Life

Q. If a log contains 60.0% of the 14C present in a living tree, how long (yr) has the log been dead? The half-life of 14C is 5715 years. Enter your an...

Solved • Dec 18, 2019

First Order Half Life

Q. Lead-200 has a half-life of 21.50 hours. Starting with 3.770 mg of this isotope, how much would remain after 72.0 hours?a. 1.09b. 0.10c. 1.29d. 2.9...

Solved • Dec 17, 2019

First Order Half Life

Q. Am95241 is used in many home smoke alarms. If 85% of the americium in a smoke detector decays in 1250 years, what is the half-life of this isotope?...

Solved • Dec 16, 2019

First Order Half Life

Q. In how many days will a sample of polonium 210 with a half-life of 138 days decay to one-fourth of the original amount?

Solved • Sep 4, 2019

First Order Half Life

Q. If a fossil bone is found to contain an eighth as much as C-14 as the bone of a living animal, what is the approximate age of the fossil? (Half-lif...

Solved • Sep 4, 2019

First Order Half Life

Q. Analysis of a quartz crystal shows it to contain 25% Uranium 235 and 75%  Lead 207. If the half life of Uranium 235 is 704 million years how old is...

Solved • Aug 27, 2019

First Order Half Life

Q. The curve to the right shows the radioactive decay of a particular sample of a nucleus called Element A. A particular nucleus survives for the firs...

Solved • Aug 27, 2019

First Order Half Life

Q. The half-life of a radioactive isotope is the amount of time it takes for a quantity of that isotope to decay to one half of its original value. (a...

Solved • Aug 6, 2019

First Order Half Life

Q. Cesium-137, a component of radioactive waste, has a half-life of 30.2 yr. If a sample of waste has an initial activity of 15.0 Ci due to cesium-137...

Solved • Jan 8, 2019

First Order Half Life

Q. It takes 4 h 39 min for a 2.00-mg sample of radium-230 to decay to 0.25 mg.What is the half-life of radium-230?

Solved • Jan 8, 2019

First Order Half Life

Q. Cobalt-60 is a strong gamma emitter that has a half-life of 5.26 yr. The cobalt-60 in a radiotherapy unit must be replaced when its radioactivity f...

Solved • Jan 8, 2019

First Order Half Life

Q. Tests on human subjects in Boston in 1965 and 1966, following the era of atomic bomb testing, revealed average quantities of about 2 pCi of plutoni...

Solved • Jan 8, 2019

First Order Half Life

Q. A 55.0 mg sample of sodium perchlorate contains radioactive chlorine-36 (whose atomic mass is 36.0 amu).If 29.6% of the chlorine atoms in the sampl...

Solved • Jan 8, 2019

First Order Half Life

Q. The synthetic radioisotope technetium-99, which decays by beta emission, is the most widely used isotope in nuclear medicine. The following data we...

Solved • Jan 8, 2019

First Order Half Life

Q. Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr.How many beta particles are emitted in 205 s by a 3.55 mg sample of 60Co?

Solved • Jan 8, 2019

First Order Half Life

Q. The cloth shroud from around a mummy is found to have a 14C activity of 9.8 disintegrations per minute per gram of carbon as compared with living o...

Solved • Jan 8, 2019

First Order Half Life

Q. A wooden artifact from a Chinese temple has a 14C activity of 37.6 counts per minute as compared with an activity of 58.2 counts per minute for a s...

Solved • Jan 8, 2019

First Order Half Life

Q. Potassium-40 decays to argon-40 with a half-life of 1.27 x 109 yr.You may want to reference (Pages 913 - 916)Section 21.4 while completing this pro...

Solved • Jan 8, 2019

First Order Half Life

Q. Radium-226, which undergoes alpha decay, has a half-life of 1600 yr.How many alpha particles are emitted in 5.00 min by a 10.0 mg sample of 226Ra?

Solved • Jan 8, 2019

First Order Half Life

Q. Decay of a 10.0-g sample of strontium-90 (t1/2 = 28.8 yr).The 10 ximes 10 grids show how much of the radioactive isotope remains aftervarious amoun...

Solved • Jan 8, 2019

First Order Half Life

Q. Plutonium-236 is an alpha emitter with a half-life of 2.86 years. How long will it take for the 1.30 mg sample of Pu-236 to decay to 0.160 mg?

Solved • Jan 8, 2019

First Order Half Life

Q. A researcher claims that an ancient scroll originated from Greek scholars in about 500 B.C. Its Carbon-14 decay rate is 92% of that found in living...

Solved • Jan 8, 2019

First Order Half Life

Q. A researcher claims that an ancient scroll originated from Greek scholars in about 500 B.C. Its Carbon-14 decay rate is 92% of that found in living...

Solved • Jan 8, 2019

First Order Half Life

Q. The contents of a rock have a 206Pb to 238U mass ratio of 0.165:1.00. Assuming that the rock did not contain any 206Pb at the time of its formation...

Solved • Jan 8, 2019

First Order Half Life

Q. Bismuth-210 is beta emitter with a half-life of 5.0 days. If a sample contains 1.3 g of Bi-210 (atomic mass = 209.984105 amu), how many beta emissi...

Solved • Jan 8, 2019

First Order Half Life

Q. Polonium-218 is an alpha emitter with a half-life of 3.0 minutes. If a sample contains 56 mg of Po-218 (atomic mass = 218.008965 amu), how many alp...

Solved • Jan 8, 2019

First Order Half Life

Q. The half-life of 232Th is 1.4 x 1010 yr. Find the number of disintegrations per hour emitted by 1.0 mol of 232Th. (Note: 1 year = 365.24 days)

Solved • Jan 8, 2019

First Order Half Life

Q. A patient is given 0.055 µg of technetium-99m, a radioactive isotope with a half-life of about 6.0 hours. How long does it take for the radioactive...

Solved • Jan 8, 2019

First Order Half Life

Q. At 8:00 A.M., a patient receives a 2.5 µg dose of I-131 to treat thyroid cancer. If the nuclide has a half-life of eight days, what mass of the nuc...

Solved • Jan 8, 2019

First Order Half Life

Q. Suppose a person ingests equal amounts of two nuclides, both of which are beta emitters (of roughly equal energy). Nuclide A has a half-life of 8.5...

Solved • Jan 8, 2019

First Order Half Life

Q. Iron-59 is a beta emitter with a half-life of 44.5 days. If a sample initially contains 164 mg of iron-59, how much iron-59 is left in the sample a...

Solved • Jan 8, 2019

First Order Half Life

Q. Suppose that an 90.0-gram laboratory animal ingested 12.0 mg of a substance that contained 2.60% by mass Pu-239, an alpha emitter with a half-life ...

Solved • Jan 8, 2019

First Order Half Life

Q. Approximately how many half-lives must pass for the amount of radioactivity in a substance to decrease to below 1% of its initial level?

Solved • Jan 8, 2019

First Order Half Life

Q. The half-life of 238U is 4.5 x 109 yr. A sample of rock of mass 1.7 g is found to produce 30 dis/s. Assuming all the radioactivity is due to 238U, ...

Solved • Jan 8, 2019

First Order Half Life

Q. A sample of F-18 has an initial decay rate of 1.6×105 /s .How long will it take for the decay rate to fall to 2.6×103 /s ? (F-18 has a half-life of...

Solved • Jan 8, 2019

First Order Half Life

Q. A sample of Tl-201 has an initial decay rate of 5.88×104 /s .How long will it take for the decay rate to fall to 303 /s ? (Tl-201 has a half-life o...

Solved • Jan 8, 2019

First Order Half Life

Q. A wooden boat discovered just south of the Great Pyramid in Egypt has a carbon-14/carbon-12 ratio that is 73.0% of that found in living organisms.H...

Solved • Jan 8, 2019

First Order Half Life

Q. Consider this graph representing the decay of a radioactive nuclide.What is the half-life of the nuclide?

Solved • Jan 8, 2019

First Order Half Life

Q. A rock that contains 3.1×10−15 mol of 232Th (t1/2 = 1.4×1010 yr) has 9.5×104 fission tracks, each track representing the fission of one atom of 232...

Solved • Jan 8, 2019

First Order Half Life

Q. A rock contains 270 μmol of 238U (t1/2 = 4.5×109 yr) and 110 μmol of 206Pb. Assuming that all the 206Pb comes from decay of the 238U, estimate the ...

Solved • Jan 8, 2019

First Order Half Life

Q. The half-life of radium-226 is 1.60×103 yr. How many hours will it take for a 2.50-g sample to decay to the point where 0.185 g of the isotope rema...

Solved • Jan 8, 2019

First Order Half Life

Q. The isotope 21283Bi has a half-life of 1.01 yr. What mass (in mg) of a 2.00-mg sample will remain after 3.75×103 h?  

Solved • Jan 8, 2019

First Order Half Life

Q. If 6.40×10−9 mol of 176W emits 1.07×1015 β+ particles in 1.00 h, what is the decay constant?

Solved • Jan 8, 2019

First Order Half Life

Q. Given specimens uranium-232 (t 1/2 = 68.9 y) and uranium-233 (t 1/2 =  159,200 y) of equal mass, which one would have greater activity and why?

Solved • Dec 12, 2018

First Order Half Life

Q. Technetium-99m has a half-life of 6.01 hours. If a patient injected with technetium-99m is safe to leave the hospital once 75% of the dose has deca...

Solved • Dec 12, 2018

First Order Half Life

Q. Plutonium was detected in trace amounts in natural uranium deposits by Glenn Seaborg and his associates in 1941. They proposed that the source of t...

Solved • Dec 11, 2018

First Order Half Life

Q. A sample of rock was found to contain 8.23 mg of rubidium-87 and 0.47 mg of strontium-87.(a) Calculate the age of the rock if the half-life of the ...

Solved • Dec 11, 2018

First Order Half Life

Q. The isotope  9038 Sr is one of the extremely hazardous species in the residues from nuclear power generation. The strontium in a 0.500-g sample dim...

Solved • Dec 11, 2018

First Order Half Life

Q. The isotope  208Tl undergoes β decay with a half-life of 3.1 min.(c) What percentage of a sample of pure  208Tl remains un-decayed after 1.0 h?

Solved • Dec 11, 2018

First Order Half Life

Q. The isotope  208Tl undergoes β decay with a half-life of 3.1 min.(b) How long will it take for 99.0% of a sample of pure 208Tl to decay?

Solved • Dec 11, 2018

First Order Half Life

Q. 239Pu is a nuclear waste byproduct with a half-life of 24,000 y. What fraction of the 239Pu present today will be present in 1000 y?

Solved • Dec 11, 2018

First Order Half Life

Q. Rubidium-87 decays by β-particle production to strontium-87 with a half-life of 4.7 X 1010 years. What is the age of a rock sample that contains 10...

Solved • Dec 6, 2018

First Order Half Life

Q. A certain radioactive nuclide has a half-life of 3.00 hours.b. Calculate the decay rate in decays/s for 1.000 mole of this nuclide.

Solved • Dec 6, 2018

First Order Half Life

Q. Define “third-life” in a similar way to “half-life,” and determine the “third-life” for a nuclide that has a half-life of 31.4 years.

Solved • Dec 6, 2018

First Order Half Life

Q. At a flea market, you’ve found a very interesting painting done in the style of Rembrandt’s “dark period” (1642–1672). You suspect that you really ...

Solved • Dec 6, 2018

First Order Half Life

Q. Americium-241 is used in smoke detectors. It has a first order rate constant for radioactive decay of k = 1.6 10–3 yr–1. By contrast, iodine-125, w...

Solved • Dec 6, 2018

First Order Half Life

Q. The images shown here depict the first-order reaction A → B at various times during the reaction process. The black circles represent reactant A an...

Solved • Dec 6, 2018

First Order Half Life

Q. The half-life for the radioactive decay of U-238 is 4.5 billion years and is independent of initial concentration.If a sample of U-238 initially co...

Solved • Dec 6, 2018

First Order Half Life

Q. A rock contains 0.688 mg  206Pb for every 1.000 mg  238U present. Assuming that no lead was originally present, that all the 206Pb formed over the ...

Solved • Dec 5, 2018

First Order Half Life

Q. The bromine-82 nucleus has a half-life of 1.0 X 10 3 min. If you wanted 1.0 g  82Br and the delivery time was 3.0 days, what mass of NaBr should yo...

Solved • Dec 5, 2018

First Order Half Life

Q. Phosphorus-32 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus...

Solved • Dec 5, 2018

First Order Half Life

Q. The curie (Ci) is a commonly used unit for measuring nuclear radioactivity: 1 curie of radiation is equal to 3.7 X 1010 decay events per second (th...

Solved • Dec 5, 2018

First Order Half Life

Q. A chemist wishing to do an experiment requiring  47Ca2+ (half-life = 4.5 days) needs 5.0 ug of the nuclide. What mass of 47CaCO3 must be ordered if...

Solved • Dec 5, 2018

First Order Half Life

Q. Radioactive copper-64 decays with a half-life of 12.8 days.b. A sample contains 28.0 mg 64Cu. How many decay events will be produced in the first s...

Solved • Dec 5, 2018

First Order Half Life

Q. The rate constant for a certain radioactive nuclide is 1.0 X 10 -3 h-1. What is the half-life of this nuclide?

Solved • Dec 5, 2018

First Order Half Life

Q. What is the half-life of an isotope that decays to 12.5% of its original activity in 48.3 hours? 

Solved • Oct 23, 2018

First Order Half Life

Q. The usefulness of radiocarbon dating is limited to objects no older than 50,000 yr. What percent of the carbon-14, originally present in a 8.0-g sa...

Solved • Oct 4, 2018

First Order Half Life

Q. Be sure to answer all parts.Archeologists can determine the age of artifacts made of wood or bone by measuring the amount of the radioactive isotop...

Solved • Sep 13, 2018

First Order Half Life

Q. Be sure to answer all parts.The radioactive potassium-40 isotope decays to argon-40 with a half-life of 1.2 x 109 years. (a) Write a balanced equat...

Solved • Aug 29, 2018

First Order Half Life

Q. Enter your answer in the provided box.Strontium-90 is one of the products of the fission of uranium-235. This strontium isotope is radioactive, wit...

Solved • Aug 29, 2018

First Order Half Life

Q. Enter your answer in the provided box.What would be the 14C activity in a 2400-year old wooden object? Assume that the 14C activity of an equal mas...

Solved • Aug 29, 2018

First Order Half Life

Q. Be sure to answer all parts.A freshly isolated sample of  90Y was found to have an activity of 1.9 x 105 disintegrations per minute at 1: 00 p.m. o...

Solved • Aug 29, 2018

First Order Half Life

Q. Be sure to answer all parts.The radioactive decay of thallium-206 to lead-206 has a half-life of 4.20 min. Starting with 4.70 x 1022 atoms of thall...

Solved • Aug 29, 2018

First Order Half Life

Q. Enter your answer in the provided box.A rock sample originally contains 4.78 mg of  238U. How much 206Pb will be in the rock sample when it is 1.7 ...

Solved • Aug 29, 2018

First Order Half Life

Q. Be sure to answer all parts.Determine the age of rock that contains 31.4 mg of  238U and 2.77 mg of  206Pb. (t1/2 of  238U = 4.51 x 109 yr). Enter ...

Solved • Aug 29, 2018

First Order Half Life

Q. Rate Constant for a First-Order Decomposition Reaction Be sure to answer all parts.In a first-order decomposition reaction, 50.0% of a compound dec...

Solved • Aug 29, 2018

First Order Half Life

Q. What is the half-life of an isotope that decays to 12.5% of its original activity in 56.6 hours?

Solved • Aug 28, 2018

First Order Half Life

Q. A sample of F-18 has an initial decay rate of 1.2 x 105/s. Part AHow long does it take for the decay rate to fall to 1.1 x 102/s? (F-18 has a half-...

Solved • Aug 22, 2018

First Order Half Life

Q. The halt-lives of different medical radioisotopes are given in the table below. If the initial amount of chromium-51 is 133 mCi, how much chromium-...

Solved • Aug 20, 2018

First Order Half Life

Q. Sodium-24 has a half-life of 14.8 hours. How much of a 751.1 mg sodium-24 sample will remain after 3.7 days?

Solved • Aug 20, 2018

First Order Half Life

Q. The half-life of Chromium-51 is 28 days. Starting with an original sample size of 12.0μg, calculate the number of days it will take for the radioac...

Solved • Aug 20, 2018

First Order Half Life

Q. What is the half-life of an isotope that decays to 3.125% of its original activity in 57.8 hours?

Solved • Jul 31, 2018

First Order Half Life

Q. Provided in the table below are two isotopes and their corresponding half-life periods. Which isotope decays the fastest and which isotope is the m...

Solved • Jul 30, 2018

First Order Half Life

Q. Consider comparing the two Phosphorous radionuclides given below and their corresponding half-life periods. Which statement below is true? a. Phosp...

Solved • Jul 30, 2018

First Order Half Life

Q. Calculate the amount of radioactive material remaining after a given period of time.The half-life of radon-222 is 3.82 days. If you begin with 40.3...

Solved • Jul 30, 2018

First Order Half Life

Q. After 60.0 min, 42.0% of a compound has decomposed. What is the half-life of this reaction assuming first-order kinetics? 

Solved • Jul 25, 2018

First Order Half Life

Q. The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 57.2% of their carb...

Solved • Jul 24, 2018

First Order Half Life

Q. You just discovered a radioactive element with an atomic mass of 250 g/mol. A sample of 5.11 ng of it decays at a rate of 3.00 atoms per second. Wh...

Solved • Jul 24, 2018