Radioactive reactions follow principles dealing with Chemical Kinetics.

Concept #1: Understanding Positron Emission.

Radioactive decay follows a 1^{st} order mechanism and so has a similar integrated rate law equation from Chemical Kinetics.

Example #1: A sample of radon-222 has an initial α particle activity (A_{0}) of 8.5 x10^{4} dps (disintegrations per second). After 7.3 days, its activity (A) is 3.7 x 10^{4} dps. What is the half-life of radon-222?

Example #2: Gallium citrate, containing the radioactive isotope gallium – 67, is used medically as a tumor seeking agent. It has a half – life of 78.2 hours. How long will it take for a sample of gallium citrate to decay to 20.0% of its original activity?

Example #3: What percentage of carbon – 14 ( t_{1/2} = 5715 years) remains in a sample estimated to be 16,230 years old?

The radioactive isotope 19O, prepared by neutron irradiation of 19F, has a half life of 29 s. What percentage of a freshly prepared sample of 19O remains after 2.00 min?
(a) 4.5%
(b) 25%
(c) 5.7%
(d) 18%
(e) 69%

The approximate date of an earthquake that occured in a remote region before recorded history is determined by measuring the 14C activity in parts of a tree uprooted by the quake. The 14C activity is 11.2 disintegrations/min•gC in the tree. A living tree has a activity of 15.3 disintegrations/min•gC. How long ago did the eathquake occur? t 1/2 of 14C = 5730 yr.
(a) 32,100 yr
(b) 1790 yr
(c) 599 yr
(d) 1580 yr
(e) 2580 yr

222Ra is a naturally occurring radioisotope that can build up in homes. Calculate the rate constant for the first‐order decay of 222Ra. ( t1/2 = 3.30 x 105 s)
A) 2.29 x 105 s‐1
B) 2.1 x 10‐6 s‐1
C) 12.7 s‐1
D) 3.03 x 10‐6 s‐1
E) 4.37 x 10‐6 s‐1

The specific activity of 14C in the biosphere is 0.255 Bq per gram, and the half-life of 14C is 5730 years. What is the age of a piece of Egyptian papyrus that shows a 14C specific activity of 0.156 Bq?
(a) 2820 years
(b) 3510 years
(c) 4060 years
(d) 5730 years
(e) 5860 years

The half-life of nickel-63 is 85 years. How old is a painting with an activity that is 3.5% of the steady-state rate for Ni-63?
a. 0.027 yr
b. 3.0 yr
c. 410 yr
d. 2400 yr

The half-life of iodine-131 is 8.04 days. Calculate the percent of an iodine sample left after exactly 2 days.
a) 84.2%
b) 82.0%
c) 67.2%
d) 6.17%
e) 57.5%

A sample of a dish from an archaeological dig gave 18,500 disintegrations per gram of carbon per day. A 1.00 g sample of carbon from a modern source gave 22,080 disintegrations per day. If the decay constant of carbon-14 is 1.2 x 10-4 y-1, what is the age of the dish?
a) 640 y
b) 8300 y
c) 68,000 y
d) 30,000 y
e) 1,500 y

The decay constant for lithium-8 is 0.825 s-1. What fraction of Li-8 remains after 0.500 s?
a) 0.662
b) 0.387
c) 0.413
d) 0.192
e) 0.0224

Charcoal samples from Stonehenge in England were burned in O2, and the resultant CO2 gas bubbled into a solution of Ca(OH)2 (limewater), resulting in the precipitation of CaCO3. The CaCO3 was removed by filtration and dried. A 791 -mg sample of the CaCO3 had a radioactivity of 1.6×10−2 Bq because of carbon-14. By comparison, living organisms undergo 15.3 disintegrations per minute per gram of carbon.Using the half-life of carbon-14,5700 yr, calculate the age of the charcoal sample.

Radon-220 undergoes alpha decay with a half-life of 55.6 s. Assume there are 16,000 atoms present initially.How many atoms are present after 0
s?

Radon-220 undergoes alpha decay with a half-life of 55.6 s. Assume there are 16,000 atoms present initially.How many atoms are present after 166.8
s?

Radon-220 undergoes alpha decay with a half-life of 55.6 s. Assume there are 16,000 atoms present initially.Calculate how many atoms will be present at 150
s.

A sample initially contains 5.2 moles of a radioactive isotope. How much of the sample
remains after four half-lives?

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?

Cobalt-60, which undergoes beta decay, has a half-life of 5.26 yr.What is the activity of the sample in Bq?

Some watch dials are coated with a phosphor, like ZnS, and a polymer in which some of the 1H atoms have been replaced by 3H atoms, tritium. The phosphor emits light when struck by the beta particle from the tritium decay, causing the dials to glow in the dark. The half-life of tritium is 12.3 yr.If the light given off is assumed to be directly proportional to the amount of tritium, by what percentage will a dial be dimmed in a watch that is 55 years old?

One of the nuclides in spent nuclear fuel is U-235, an alpha emitter with a half-life of 703 million years.How long will take for the amount of U-235 to reach 41.0 % of its initial amount?

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 1.83 hours.)

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 of 3.042 days.)

A layer of peat beneath the glacial sediments of the last ice age has a carbon-14/carbon-12 ratio that is 22.6% of that found in living organisms.How long ago was this ice age?

PET studies require fluorine-18, which is produced in a cyclotron and decays with a half-life of 1.83 hours.Assuming that the F-18 can be transported at 60.0 miles/hour, how close must the hospital be to the cyclotron if 66% of the F-18 produced is to make it to the hospital?

Iodine-131 is a convenient radioisotope to monitor thyroid activity in humans. It is a beta emitter with a half-life of 8.02 days. The thyroid is the only gland in the body that uses iodine. A person undergoing a test of thyroid activity drinks a solution of NaI, in which only a small fraction of the iodide is radioactive.A normal thyroid will take up about 12% of the ingested iodide in a few hours. How long will it take for the radioactive iodide taken up and held by the thyroid to decay to 0.01% of the original amount?

The synthetic radioisotope technetium-99, which decays by beta emission, is the most widely used isotope in nuclear medicine. The following data were collected on a sample of 99Tc:
Disintegrations per Minute
Time (h)
180
0
130
2.5
104
5.0
77
7.5
59
10.0
46
12.5
24
17.5
Using these data, make an appropriate graph and curve fit to determine the half-life.

A 26.10 g sample of water containing tritium, 13 H, emits 1550 beta particles per second. Tritium is a weak beta emitter, with a half-life of 12.3 yr.What fraction of all the hydrogen in the water sample is tritium? [ Hint: Use equations large{{
m ln} frac{N_t}{N_0} = kt} and large{k=frac{0.693}{t_{1/2}}}.]

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 sample are chlorine-36 and the remainder is naturally occurring nonradioactive chlorine atoms, how many disintegrations per second are produced by this sample? The half-life of chlorine-36 is 3.0 105 yr.

A sample of an alpha emitter having an activity of 0.21 Ci is stored in a 25.2 mL sealed container at 22oC for 245 days.How many alpha particles are formed during this time?

A sample of an alpha emitter having an activity of 0.21 Ci is stored in a 25.2 mL sealed container at 22oC for 245 days.Assuming that each alpha particle is converted to a helium atom, what is the partial pressure of helium gas in the container after this 245-day period?

A 25.0-mL sample of 0.050 M barium nitrate solution was mixed with 25.0 mL of 0.050 M sodium sulfate solution labeled with radioactive sulfur-35. The activity of the initial sodium sulfate solution was 1.22 106 Bq/mL. After the resultant precipitate was removed by filtration, the remaining filtrate was found to have an activity of 250 Bq/mL.Calculate the Ksp for the precipitate under the conditions of the experiment.

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

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

Each statement below refers to a comparison between two radioisotopes, A and X. Indicate whether each of the following statements is true or false, and why.If the half-life for A is shorter than the half-life for X, A has a larger decay rate constant.

Each statement below refers to a comparison between two radioisotopes, A and X. Indicate whether each of the following statements is true or false, and why.If X is "not radioactive," its half-life is essentially zero.

Each statement below refers to a comparison between two radioisotopes, A and X. Indicate whether each of the following statements is true or false, and why.If A has a half-life of 10 years, and X has a half-life of 10,000 years, A would be a more suitable radioisotope to measure processes occurring on the 40-year time scale.

Estimate the half-life of the isotope from the graph below.A. 1920 daysB. 1280 daysC. 960 daysD. 640 daysE. 320 days

All the stable isotopes of boron, carbon, nitrogen, oxygen, and fluorine are shown in the chart in the right hand column (in red), along with their radioactive isotopes with t1/2 > 1 min (in blue).Which isotope would decay to 12.5 % of its original concentration after 1 hour?

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 isotope to decay to 3.5×10−3 g ? (Assume no excretion of the nuclide from the body.)

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 nuclide remains in the patient at 6:00 P.M. the next day? (Assume no excretion of the nuclide from the body.)

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, how long will it take for the activity due to cesium-137 to drop to 0.250 Ci?

An ancient skull has a carbon-14 decay rate of 0.86 disintegrations per minute per gram of carbon (0.86 dis/min • g C). (Assume that living organisms have a carbon-14 decay rate of 15.3 dis/min • g C and that carbon-14 has a half-life of 5730 yr.)How old is the skull?

Cesium-137, which has a half-life of 30.2 yr, is a component of the radioactive waste from nuclear power plants. If the activity due to cesium-137 in a sample of radioactive waste has decreased to 35.2% of its initial value, how old is the sample?

A rock from Australia contains 0.439 g of Pb-206 to every 1.00 g of U-238. Assuming that the rock did not contain any Pb-206 at the time of its formation, how old is the rock?

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?

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 emissions would occur in 13.6 days?

Bismuth-210 is beta emitter with a half-life of 5.0 days. If a sample contains 1.2 g of Bi-210 (atomic mass = 209.984105 amu), how many beta emissions occur in 13.5 days? If a person's body intercepts 5.5 % of those emissions, to what dose of radiation (in Ci) is the person exposed?

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 alpha emissions occur in 26.0 minutes?

Polonium-218 is an alpha emitter with a half-life of 3.0 minutes. If 55 mg of Po-218 (atomic mass = 218.008965 amu) is ingested by a person, to what amount of radiation (in Ci) is the person exposed?

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)

The nuclide 38Cl decays by beta emission with a half-life of 37.2 min. A sample of 0.40 mol of H38Cl is placed in a 6.01 L container. After 74.4 min the pressure is 1650 mmHg. What is the temperature of the container?

When 10BF3 is bombarded with neutrons, the boron-10 undergoes an α decay, but the F is unaffected. A 0.31-mol sample of 10BF3 contained in a 4.1-L container at 298 K is bombarded with neutrons until half of the 10BF3 has reacted. What is the pressure in the container at 298 K?

A person is exposed for three days to identical amounts of two different nuclides that emit positrons of roughly equal energy. The half-life of nuclide A is 18.5 days and the half-life of nuclide B is 239 days. Which of the two nuclides poses the greater health risk?

An artifact has a carbon-14 decay rate of 8.56 disintegrations per minute per gram of carbon (8.56 dis/min • g C ). Living organisms have carbon-14 decay rate of 15.3 dis/min • g C. The half-life of carbon-14 is 5730 yr. How old is the artifact?

A radioactive sample contains 1.60 g of an isotope with a half-life of 3.8 days. What mass of the isotope will remain after 5.7 days? (Assume no excretion of the nuclide from the body.)

A radioisotope of technetium is useful in medical imaging techniques. A sample initially contains 80.0 mg of this isotope. After 24.0 h, only 5.0 mg of the technetium isotope remains. What is the half-life of the isotope?

A mammoth skeleton has a carbon-14 decay rate of 0.49 disintegrations per minute per gram of carbon (0.49 dis/min • g C ). When did the mammoth live? (Assume that living organisms have a carbon-14 decay rate of 15.3 dis/min • g C and that carbon-14 has a half-life of 5715 yr.)

If one-trillionth of the atoms of a radioactive isotope disintegrate each day, what is the decay constant of the process?

If 2.8×10−10% of the atoms of a radioactive isotope disintegrate in 1.0 yr, what is the decay constant of the process?

If 1.00×10−12 mol of 135Cs emits 1.39×105 β− particles in 1.00 yr, what is the decay constant?

A patient ingests 1.53 mg of 131I (Iodine-131), a beta emitter with a half-life of 8.0 days. Assuming that none of the 131I is eliminated from the person's body in the first 4.0 hours of treatment, what is the exposure (in Ci) during those first four hours?

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

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?

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 remains?

Some nuclear power plants use plutonium-239, which is produced in breeder reactors. The rate-determining step is the second β− emission. How long does it take to make 1.00 kg of 239Pu if the reaction is complete when the product is 90.% 239Pu?

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 rock’s age.

A fabric remnant from a burial site has a 14C/12C ratio of 0.735 of the original value. How old is the fabric?

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, determine the age of the rock. Uranium-238 decays to lead-206 with a half-life of 4.5 billion years.

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?

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 232Th. How old is the rock?

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 organisms. How old is the scroll? (The half-life of Carbon-14 is 5730 yr)

A volcanic eruption melts a large chunk of rock, and all gases are expelled. After cooling, 1840Ar accumulates from the ongoing decay of 1940K in the rock (t1/2 = 1.25×109 yr). When a piece of rock is analyzed, it is found to contain 1.38 mmol of 40K and 1.14 mmol of 40Ar. How long ago did the rock cool?

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 organisms. Could it be authentic? (The half-life of Carbon-14 is 5730 yr)

A 1.00 × 10 –6-g sample of nobelium, 254102 No, has a half-life of 55 seconds after it is formed. What is the percentage of 254102 No remaining at the following times?(a) 5.0 min after it forms

A 1.00 × 10 –6-g sample of nobelium, 254102 No, has a half-life of 55 seconds after it is formed. What is the percentage of 254102 No remaining at the following times?(b) 1.0 h after it forms

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?

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?

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?

If 1.000 g of 22688Ra produces 0.0001 mL of the gas 22286 Rn at STP (standard temperature and pressure) in 24 h, what is the half-life of 226Ra in years?

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 diminishes to 0.393 g in 10.0 y. Calculate the half-life.

Uranium-238 undergoes a slow decay step (t1/2 = 4.5×109 yr) followed by a series of fast steps to form the stable isotope 206Pb. Thus, on a time scale of billions of years, 238U effectively decays “directly” to 206Pb, and the relative amounts of these isotopes are used to find the age of some rocks. Two students derive equations relating number of half-lives (n) since the rock formed to the amounts of the isotopes:(a) Which equation is correct, and why?(b) If a rock contains exactly twice as much 238U as 206Pb, what is its age in years?

What is the age of mummified primate skin that contains 8.25% of the original quantity of 14C?

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 decay of rubidium by β emission is 4.7 × 10 10 y.

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 decay of rubidium by β emission is 4.7 × 10 10 y.(b) If some 8738 Sr was initially present in the rock, would the rock be younger, older, or the same age as the age calculated in (a)? Explain your answer.

A sample of cobalt-60 (t1/2 = 5.27 yr), a powerful γ emitter used to treat cancer, was purchased by a hospital on March 1, 2012. The sample must be replaced when its activity reaches 70.% of the original value. On what date must it be replaced?

A laboratory investigation shows that a sample of uranium ore contains 5.37 mg of 23892 U and 2.52 mg of 20682Pb. Calculate the age of the ore. The half-life of 23892 U is 4.5 × 109 yr.

Isotope such as 26Al (half-life: 7.2 × 10 5 years) are believed to have been present in our solar system as it formed, but have since decayed and are now called extinct nuclide.(b) The earth was formed about 4.7 × 10 9 (4.7 billion) years ago. How old was the earth when 99.999999% of the 26Al originally present had decayed?

An ancient sword has a blade from the early Roman Empire, around 100 ad, but the wooden handle, inlaid wooden decorations, leather ribbon, and leather sheath have different styles. Given the following activities, estimate the age of each part. Which part was made near the time of the blade (t1/2 of 14C =5730 yr; 𝒜0 = 15.3 d/min·g)?

Americium-241 is widely used in smoke detectors. The radiation released by this element ionizes particles that are then detected by a charged-particle collector. The half-life of 241Am is 433 years, and it decays by emitting α particles. How many α particles are emitted each second by a 5.00-g sample of 241Am?

Archeologists removed some charcoal from a Native American campfire site, burned it in O2, and bubbled the CO2 formed into Ca(OH)2 solution (limewater). The CaCO3 that precipitated was filtered and dried. If 4.58 g of the CaCO3 had a radioactivity of 3.2 d/min, how long ago was the campfire burning?

Krypton consists of several radioactive isotopes, some of which are listed in the following table.Which of these isotopes is most stable, and which isotope is “hottest”? How long does it take for 87.5% of each isotope to decay?

A layer of peat beneath the glacial sediments of the last ice age has a carbon-14/carbon-12 ratio that is 22.6% of that found in living organisms. How long ago was this ice age?

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 second? Assume the atomic mass of 64Cu is 64.0 u.

Radioactive copper-64 decays with a half-life of 12.8 days.c. A chemist obtains a fresh sample of 64Cu and measures its radioactivity. She then determines that to do an experiment, the radioactivity cannot fall below 25% of the initial measured value. How long does she have to do the experiment?

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 it takes 48 h for delivery from the supplier? Assume that the atomic mass of 47Ca is 47.0 u.

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 (the number of decay events from 1 g radium in 1 s). a. What mass of Na 238SO4 has an activity of 10.0 mCi? Sulfur-38 has an atomic mass of 38.0 u and a half-life of 2.87 h.

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 (the number of decay events from 1 g radium in 1 s). a. What mass of Na238SO4 has an activity of 10.0 mCi? Sulfur-38 has an atomic mass of 38.0 u and a half-life of2.87 h.b. How long does it take for 99.99% of a sample of sulfur-38 to decay?

The first atomic explosion was detonated in the desert north of Alamogordo, New Mexico, on July 16, 1945. What percentage of the strontium-90 (t1/2 = 28.9 years) originally produced by that explosion still remains as of July 16, 2015?

What fraction of the 235U (t1/2 = 7.0×108 yr) created when Earth was formed would remain after 2.8×109 yr?

Iodine-131 is used in the diagnosis and treatment of thyroid disease and has a half-life of 8.0 days. If a patient with thyroid disease consumes a sample of Na131I containing 10. ug 131I, how long will it take for the amount of 131I to decrease to 1/100 of the original amount?

238U (t1/2 = 4.5×109 yr) begins a decay series that ultimately forms 206Pb. The scene below depicts the relative number of 238U atoms (red) and 206Pb atoms (green) in a mineral. If all the Pb comes from 238U, calculate the age of the sample.

Technetium-99 has been used as a radiographic agent in bone scans ( 9943Tc is absorbed by bones). If 9943Tc has a half-life of 6.0 hours, what fraction of an administered dose of 100. ug 9943Tc remains in a patient’s body after 2.0 days?

Technetium-99m is a metastable nuclide used in numerous cancer diagnostic and treatment programs. It is prepared just before use because it decays rapidly through γ emission:99mTc ⟶ 99Tc + γUse the data below to determine(a) the half-life of 99mTc;

Phosphorus-32 is a commonly used radioactive nuclide in biochemical research, particularly in studies of nucleic acids. The half-life of phosphorus-32 is 14.3 days. What mass of phosphorus-32 is left from an original sample of 175 mg Na332PO4 after 35.0 days? Assume the atomic mass of 32P is 32.0 u.

Technetium-99m is a metastable nuclide used in numerous cancer diagnostic and treatment programs. It is prepared just before use because it decays rapidly through γ emission:99mTc ⟶ 99Tc + γUse the data below to determine(a) the half-life of 99mTc;(b) the percentage of the isotope that is lost if it takes 2.0 h to prepare and administer the dose.

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 you order (assuming all of the Br in the NaBr was 82Br)?

How many curies are produced by 1.0 mol of 40K (t1/2 = 1.25×109 yr)? How many becquerels?

Fresh rainwater or surface water contains enough tritium ( 31H ) to show 5.5 decay events per minute per 100. g water. Tritium has a half-life of 12.3 years. You are asked to check a vintage wine that is claimed to have been produced in 1946. How many decay events per minute should you expect to observe in 100. g of that wine?

The fraction of a radioactive isotope remaining at time t is ( 1/2) t/t1/2 , where t1/2 is the half-life. If the half-life of carbon-14 is 5730 yr, what fraction of carbon-14 in a piece of charcoal remains after(a) 10.0 yr;

A living plant contains approximately the same fraction of carbon-14 as in atmospheric carbon dioxide. Assuming that the observed rate of decay of carbon-14 from a living plant is 13.6 counts per minute per gram of carbon, how many counts per minute per gram of carbon will be measured from a 15,000-year-old sample? Will radiocarbon dating work well for small samples of 10 mg or less? (For 14C, t1/2 = 5730 years.)

The fraction of a radioactive isotope remaining at time t is ( 1/2) t/t1/2 , where t1/2 is the half-life. If the half-life of carbon-14 is 5730 yr, what fraction of carbon-14 in a piece of charcoal remains after(b) 10.0×103 yr;

Assume a constant 14C/12C ratio of 13.6 counts per minute per gram of living matter. A sample of a petrified tree was found to give 1.2 counts per minute per gram. How old is the tree? (For 14C, t1/2 = 5730 years.)

The fraction of a radioactive isotope remaining at time t is ( 1/2) t/t1/2 , where t1/2 is the half-life. If the half-life of carbon-14 is 5730 yr, what fraction of carbon-14 in a piece of charcoal remains after(c) 10.0×104 yr?

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 years has remained in the rock, and that the number of nuclides in intermediate stages of decay between 238U and 206Pb is negligible, calculate the age of the rock. (For 238U, t1/2 = 4.5 X 10 9 years.)

The fraction of a radioactive isotope remaining at time t is ( 1/2) t/t1/2 , where t1/2 is the half-life. If the half-life of carbon-14 is 5730 yr, what fraction of carbon-14 in a piece of charcoal remains after(a) 10.0 yr;(b) 10.0×103 yr;(c) 10.0×104 yr?(d) Why is radiocarbon dating more reliable for the fraction remaining in part (b) than that in part (a) or in part (c)?

In the 1950s, radioactive material was spread over the land from aboveground nuclear tests. A woman drinks some contaminated milk and ingests 0.0500 g of 90Sr, which is taken up by bones and teeth and not eliminated. (a) How much 90Sr (t1/2 = 29 yr) is present in her body after 10 yr?

In the 1950s, radioactive material was spread over the land from aboveground nuclear tests. A woman drinks some contaminated milk and ingests 0.0500 g of 90Sr, which is taken up by bones and teeth and not eliminated.(a) How much 90Sr (t1/2 = 29 yr) is present in her body after 10 yr?(b) How long will it take for 99.9% of the 90Sr that she ingested to decay?

What volume of radon will be produced per hour at STP from 1.000 g of 226Ra (t1/2 = 1599 yr; 1 yr = 8766 h; mass of one 226Ra atom = 226.025402 amu)?

90Kr (t1/2 = 32 s) is used to study respiration. How soon after being made must a sample be administered to the patient if the activity must be at least 90% of the original activity?

The accompanying graph illustrates the decay of 4288Mo, which decays via positron emission.What fraction of the original sample of 4288Mo remains after 12 minutes?

How much time is required for a 6.30 mg sample of 51Cr to decay to 0.700 mg if it has a half-life of 27.8 days?

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 organisms that undergo 16.3 disintegrations per minute per gram of carbon.From the half-life for 14C decay, 5715 yr, calculate the age of the shroud.

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 standard of zero age.From the half-life for 14C decay, 5715 yr, determine the age of the artifact.

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 problem.What is the age of a rock in which the mass ratio of 40Ar to 40K is 4.2?

The half-life for the process 238 U → 206 Pb is 4.5 109yr. A mineral sample contains 71.0 mg of 238 U and 16.5 mg of 206 Pb.What is the age of the mineral?

A meteor has a Pb-206:U-238 mass ratio of 0.850:1.00. What is the age of the meteor? (Assume that the meteor did not contain any Pb206 at the time of its formation.)

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 do not have a genuine Rembrandt, but you take it to the local university for testing. Living wood shows a carbon-14 activity of 15.3 counts per minute per gram. Your painting showed a carbon-14 activity of 15.1 counts per minute per gram. Could it be a genuine Rembrandt?

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 decayed, when is the patient allowed to leave?

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.

A proposed system for storing nuclear wastes involves storing the radioactive material in caves or deep mine shafts. One of the most toxic nuclides that must be disposed of is plutonium-239, which is produced in breeder reactors and has a half-life of 24,100 years. A suitable storage place must be geologically stable long enough for the activity of plutonium-239 to decrease to 0.1% of its original value. How long is this for plutonium-239?

Iodine that enters the body is stored in the thyroid gland from which it is released to control growth and metabolism. The thyroid can be imaged if iodine-131 is injected into the body. In larger doses, I-133 is also used as a means of treating cancer of the thyroid. I-131 has a half-life of 8.70 days and decays by β− emission.(b) How long will it take for 95.0% of a dose of I-131 to decay?

During World War II, tritium ( 3H) was a component of fluorescent watch dials and hands. Assume you have such a watch that was made in January 1944. If 17% or more of the original tritium was needed to read the dial in dark places, until what year could you read the time at night? (For 3H, t1/2 = 12.3 yr.)

A laboratory rat is exposed to an alpha-radiation source whose activity is 13.6 mCi .What is the activity of the radiation in disintegrations per second?

Radium-226 (atomic mass = 226.025402 amu) decays to radon-224 (a radioactive gas) with a half-life of 1.6 x 103 years. What volume of radon gas (at 25.0 ˚C and 1.0 atm) is produced by 26.0 g of radium in 5.5 days?

Iodine-131 has a half-life of 8.0 days. How many days will it take for 174 g of 131I to decay to 83 g of 131I?

Carbon from the remains of an extinct Australian marsupial, called Diprotodon, has a specific activity of 0.61 pCi/g. Modern carbon has a specific activity of 6.89 pCi/g. How long ago did the Diprotodon apparently become extinct?

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 109.7 ug of 87Rb and 3.1 ug of 87Sr? Assume that no 87Sr was present when the rock was formed. The atomic masses for 87Rb and 87Sr are 86.90919 u and 86.90888 u, respectively.

Tritium (3H; t1/2 = 12.26 yr) is continually formed in the upper troposphere by interaction of solar particles with nitrogen. As a result, natural waters contain a small amount of tritium. Two samples of wine are analyzed, one known to be made in 1941 and another made earlier. The water in the 1941 wine has 2.23 timesas much tritium as the water in the other. When was the other wine produced?

An earthquake in the area of present-day San Francisco is to be dated by measuring the 14C activity (t1/2 = 5730 yr) of parts of a tree uprooted during the event. The tree parts have an activity of 12.9 d/min·g C, and a living tree has an activity of 15.3 d/min·g C. How long ago did the earthquake occur?

According to current regulations, the maximum permissible dose of strontium-90 in the body of an adult is 1 μCi mu {
m{Ci}}(1 x 10-6 Ci).Using the relationship rate = kN, calculate the number of atoms of strontium-90 to which this dose corresponds. To what mass of strontium-90 does this correspond? The half-life for strontium-90 is 28.8 yr.

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, find the percent by mass of 238U in the rock.

Nuclear disarmament could be accomplished if weapons were not “replenished.” The tritium in warheads decays to helium with a half-life of 12.26 yr and must be replaced or the weapon is useless. What fraction of the tritium is lost in 5.50 yr?

A 1.50-L gas sample at 726 mmHg and 25.0 ˚C contains 5.51 % radon-220 by volume. Radon-220 is an alpha-emitter with a half-life of 55.6 s. How many alpha particles are emitted by the gas sample in 7.00 minutes?

A 226 mL sample of an aqueous solution contains 3.05% MgCl2 by mass (molar mass of MgCl2 is 96.9 g/mol). Exactly one-half of the magnesium ions are Mg-28, a beta emitter with a half-life of 21 hours. What is the decay rate of Mg-28 in the solution after 4.00 days? (Assume a density of 1.02 g/mL for the solution.)

The Sun radiates energy into space at the rate of 3.9 x 1026 J/s.Calculate the rate of mass loss from the Sun in kg/s.

Uranium and radium are found in many rocky soils throughout the world. Both undergo radioactive decay, and one of the products is radon-222, the heaviest noble gas (t1/2 = 3.82 days). Inhalation of this gas contributes to many lung cancers. According to the Environmental Protection Agency, the level of radioactivity from radon in homes should not exceed 4.0 pCi/L of air.(a) What is the safe level of radon in Bq/L of air?(b) A home has a radon measurement of 41.5 pCi/L. The owner vents the basement in such a way that no more radon enters the living area. What is the activity of the radon remaining in the room air (in Bq/L) after 9.5 days?(c) How many more days does it take to reach the EPA recommended level?

The half-life of 235U, an alpha emitter, is 7.1 x 108 yr. Calculate the number of alpha particles emitted by 5.5 mg of this nuclide in 1 minute.

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 plutonium radioactivity in the average person.How many disintegrations per second does this level of activity imply?

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 plutonium radioactivity in the average person.If each alpha particle deposits 8 x 10 - 13 J of energy and if the average person weighs 76 kg , calculate the number of rads and rems of radiation in 4 yr from such a level of plutonium.

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 of 24,110 years. What is the animal's initial radiation exposure in Curies?

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 of 24,110 years. If all of the energy from the emitted alpha particles is absorbed by the animal's tissues, and if the energy of each emission is 7.77 x 10–12 J, what is the dose in rads to the animal in the first 4.5 hours following the ingestion of the radioactive material?

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 of 24,110 years. Assuming a biological effectiveness factor of 20, what is the 4.5-hour dose in rems?

The hydride of an unstable nuclide of a Group IIA metal, MH2(s), decays by α-emission. A 0.025-mol sample of the hydride is placed in an evacuated 1.5 L container at 298 K. After 75 minutes, the pressure in the container is 0.46 atm{
m atm}.Find the half-life of the nuclide.

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 after 267 days?

An igneous rock contains a Pb-206/U-238 mass ratio of 0.372. How old is the rock? (U-238 decays into Pb-206 with a half-life of 4.50 x 109 yr.)

For the reaction 146 C ⟶ 147 N + ?, if 100.0 g of carbon reacts, what volume of nitrogen gas (N2) is produced at 273K and 1 atm?

The chart shows the mass of a decaying nuclide versus time.What is the half-life of the decay?

Plutonium-239 (t1/2 = 2.41×104 yr) represents a serious nuclear waste hazard. If seven half-lives are required to reach a tolerable level of radioactivity, how long must 239Pu be stored?

Uranium-238 undergoes a slow decay step (t1/2 = 4.5×109 yr) followed by a series of fast steps to form the stable isotope 206Pb. Thus, on a time scale of billions of years, 238U effectively decays “directly” to 206Pb, and the relative amounts of these isotopes are used to find the age of some rocks. Two students derive equations relating number of half-lives (n) since the rock formed to the amounts of the isotopes:(a) Which equation is correct, and why?

Technetium-99 is often used for assessing heart, liver, and lung damage because certain technetium compounds are absorbed by damaged tissues. It has a half-life of 6.0 h. Calculate the rate constant for the decay of 9943 Tc.

Plutonium was detected in trace amounts in natural uranium deposits by Glenn Seaborg and his associates in 1941. They proposed that the source of this 239Pu was the capture of neutrons by 238U nuclei. Why is this plutonium not likely to have been trapped at the time the solar system formed 4.7 × 109 years ago?

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

A 5.4-μg sample of 226RaCl2 has a radioactivity of 1.5×105 Bq. Calculate t1/2 of 226Ra

Radioactive copper-64 decays with a half-life of 12.8 days.a. What is the value of k in s -1?

The accompanying graph illustrates the decay of 4288Mo, which decays via positron emission.What is the half-life of the decay?

The accompanying graph illustrates the decay of 4288Mo, which decays via positron emission.What is the rate constant for the decay?

Radium-226, which undergoes alpha decay, has a half-life of 1600 yr.(a) How many alpha particles are emitted in 5.0 min by a 10.0-mg sample of 226Ra?(b) What is the activity of the sample in mCi?

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, which is used to test for thyroid functioning, has a rate constant for radioactive decay of k = 0.011 day–1.What is the half-life of iodine-125?

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?

A scientist is studying a 2.234 g sample of thorium-229 (t1/2 = 7340 y) in a laboratory.(a) What is its activity in Bq?

A scientist is studying a 2.234 g sample of thorium-229 (t1/2 = 7340 y) in a laboratory.(b) What is its activity in Ci?

Given specimens neon-24 (t1/2 = 3.38 min) and bismuth-211 (t 1/2 = 2.14 min) of equal mass, which one would have greater activity and why?

A certain radioactive nuclide has a half-life of 3.00 hours.a. Calculate the rate constant in s -1 for this nuclide.

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.

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 falls to 75% of the original sample.If an original sample was purchased in June 2013, when will it be necessary to replace the cobalt-60?

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.How old is the boat?

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) The half-life of radiocarbon or Carbon 14 (C-14) is 5230 years. Determine its decay rate parameter. Carbon dating is a method of determining the age of an object using the properties of radiocarbon. It was pioneered by Willard Libby and collaborators in 1949 to date archaeological, geological, and other samples. Its main idea is that by measuring the amount of radiocarbon still found in the organic matter and comparing it to the amount normally found in living matter, we can approximate the amount of time since death occurred. (b) Using the decay-rate parameter found in part (a), find the time since death if 35% of radiocarbon is still in the sample.

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 contained 1.6×1018 atoms when the universe was formed 13.8 billion years ago, how many U-238 atoms will it contain today?

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 first five hours, what's the probability that particular nucleus of Element A will decal between hours 5 and 10? What is the probability that particular nucleus of element A will decay between 5 and 20 hours?

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 the quartz crystal?

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-life of C-14 = 5715 years)

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?

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 amounts of time.If we start with a 50.0-g sample, how much of it remains after three half-lives have passed?

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?

When a 2.50 g sample of cobalt-60 is stored for 10 years, 0.669 g remain. What is the half-life of cobalt-60? a) 26.3 yb) 12.1 yc) 11.5 yd) 2.59 ye) 5.25 y

The half-lives of different medical radioisotopes are given in the table below. If the initial amount of arsenic-74 is 2.3 mCi, how much arsenic-74 (mCi) is left in the body after 54 days?

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 hours and Nuclide B has a
half-life of 15.0 hours. Both nuclides are eliminated from the body within 24 hours of
ingestion. Which of the two nuclides produces the greater radiation dose?

A moon rock collected by a U.S. Apollo mission is estimated to be 4.30 billion years old by uranium/lead dating. Assuming that the rock did not contain any lead when it was formed, what is the current mass in grams of 206Pb per 1.260 g of 236U in the rock? The half-life of 236U is t1/2 = 4.47 x 109 years.

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 radioactive isotope to drop to 1.50μg.

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 decomposes in 17.5 min. (a) What is the rate constant of the reaction? (round to four decimal places) k = _________ min-1 (b) How long does it takes for 90.0% of the compound to decompose? (round to one decimal place)

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. on December 3, 2006. At 2: 15 p.m. on December 17, 2006, its activity was measured again and found to be 5.0 x 103 disintegrations per minute. Calculate the half-life of 90Y. Enter your answer in scientific notation.

Geologists can estimate the age of rocks by their uranium-238 content. The uranium is incorporated in the rock as it hardens and then decays with first-order kinetics and a half-life of 4.5 billion years. A rock is found to contain 84.3% of the amount of uranium-238 that it contained when it was formed. (The amount that the rock contained when it was formed can be deduced from the presence of the decay products of U-238.) Part AHow old is the rock? Express your answer using two significant figures.

An old asteroid is found. A rock from it yields 1.84 g of 238U92 and 4.22 g of 206Pb82. The molar mass of 206Pb82 is 205.974 g/mol, the molar mass of 238U92 is 238.029 g/mol, and the half-life of 238U92 is 4.46 x 109 years. How old is this asteroid? Express your answer with the appropriate units.

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 x 108 years old?

The reaction below is first order in [H 2O2]: 2H2O2 (I) → 2H2O (I) + O2 (g) A solution originally at 0.600 M H2O2 is found to be 0.075 M after 54 min. The half-life for this reaction is ___________min.

The half-lives of different radioisotopes are given in the table below. How long would it take (in minutes) for the amount of lead-196 to decrease from 44.0 mg to 5.50 mg?

One of the nuclides in spent nuclear fuel is U 235, an alpha emitter with a half-life of 703 million years.How long will take for the amount of U-235 to reach 44.0 of its initial amount?

half-lives of different radioisotopes are given in the table below. If the initial amount of lead-196 is 8.0 g, how much lead-196 is left in the body after 74 minutes?

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 equation for the reaction. (b) A sample of moon rock is found to contain 16 percent potassium-40 and 84 percent argon by mass. Calculate the age of rock in years. (Assume that all the argon in the sample is the result of potassium decay.) Enter your answer in scientific notation.

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 mass of fresh-cut wood is 17.9 disintegration per second.

Be sure to answer all parts.Given that the half-life of 238U is 4.51 x 109 years, determine the age of rock found to contain 2.66 g of 238U and 0.02 g of 206Pb. Enter your answer in scientific notation. (Be sure to report your answer to the correct number of significant figures)

Some watch dials are coated with a phosphor, like ZnS, and a polymer in which some of the 1H atoms have been replaced by 3H atoms, tritium. The phosphor emits light when struck by the beta particle from the tritium decay, causing the dials to glow in the dark. The half-life of tritium is 12.3 yr. If the light given off is assumed to be directly proportional to the amount of tritium, by how many percents will a dial be dimmed in a watch that is 85 years old?Express your answer to two significant figures and include the appropriate units.

The half-life of oxygen 15 is 124 s. If a sample of oxygen 15 has an activity of 4000 Bq, how many minutes will elapse before it has an activity of 500 Bq? Express your answer to three significant figures and include the appropriate units.

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 mass of fresh-cut wood is 15.0 disintegration per second. The half-life of carbon-14 is 5,715 years.

A fossil is found to have a 14C level of 94.0% compared to living organisms. How old is the fossil?

Fluorine-18 has a half life of 110 minutes, what percent is left after 300 minutes?

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 isotope 14C present in the object. The amount of isotope decreases in a first-order process. If 15.1% of the original amount of 14C is present in a wooden tool at the time of analysis, what is the age of the tool? The half-life of 14C is 5,730 yr. Give your answer in scientific notation.

The rate constant of a first-order process that has a half-life of 3.50 min is _____ s -1.

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

lodine-131 is a radioactive isotope. After 3.00 days, 77.2% of a sample of 131I remains. What is the half-life of 131I?

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 thallium-206, calculate the number of such atoms left after 42.0 min. Enter your answer in scientific notation.

Given that the half-life of 238U is 4.51 x 109 years, determine the age of rock found to contain 2.47 g of 238U and 0.05 g of 206Pb. Enter your answer in scientific notation.(Be sure to report your answer to the correct number of significant figures)

Gallium-67 is a radioactive isotope used in treatment of lymphomas. If73.5% of a 67Ga sample remains in the patient 1.61 days after injection, what is the half-life of 67Ga

A patient is given 0.050 mg of technetium-99 m (where m means metastable - an unstable but long-lived state), a radioactive isotope with a half-life of about 6.0 hours. How long in hours until the radioactive isotope decays to 6.3 x 10-3 mg? Express your answer using two significant figures.

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, with a half-life of 28.1 years. Calculate how long (in years) it will take for 7.47 g of the isotope to be reduced to 0.141 g by decay.

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 carbon-14. How old were the bones at the time they were discovered? The bones were about ___________ years old. (Round to the nearest integer as needed.)

If the amount of 51, used to label red blood cells, in a sample decreases from 1.6 mg to 0.40 mg in 55.4 days, what is the half-life of chromium 51? Express your answer using three significant figures.

Calculate n (in 2008) for carbon-14 in charred plant remains for two different eruptions of Mt. Vesuvius, 472 AD and 512 AD. (t1/2 for 14C = 5730 y)

The half-lives of different radioisotopes are given in the table below. If the initial amount of argon-44 is 8.4 g, how much argon-44 is left in the body after 24 minutes?

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 your answer in scientific notation.

After 45.0 min, 32.0% of a compound has decomposed. What is the half-life of this reaction assuming first-order kinetics?

The half-life for the radioactive decay of C-14 is 5730 years. How long will it take for 30% of the C-14 atoms in a sample of C-14 to decay? Express your answer using two significant figures. If a sample of C-14 initially contains 1.2 mmol of C-14, how many millimoles will be left after 2260 year Express your answer in millimoles using two significant figures.

A 50.0 mg sample of an unknown radioactive substance was placed in storage and its mass measured periodically. After 18.9 days, the amount of radioactive substance had decreased to 3.13 mg What is the half-life of the unknown radioactive substance?

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 sample, remains after this period of time? The half-ife of carbon-14 is 5.73 x 103 yr.

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 mg of this isotope, what mass remains after 4.43-days have passed?

Be sure to answer all parts.A freshly isolated sample of 90Y was found to have an activity of 1.1 x 10 5 disintegrations per minute at 1:00 p.m. on December 3, 2006. At 2:15 p.m. on December 17, 2006, its activity was measured again and found to be 2.9 x 103 disintegrations per minute. Calculate the half life of 90Y. Enter your answer in scientific notation.

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. What is its half-life, in years? Use 6.022 x 1023 for Avogadro's number and 365.25 for the number of days in a year.

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?

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-51 is left in the body after 84 days?

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-life of 1.83 hours.)

Calculate the percent activity of the radioactive isotope cobalt-60 remaining after 4 half-lives.

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

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

A fossil is found to have a 14C level of 71.0% compared to living organisms. How old is the fossil?

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

Consider comparing the two Phosphorous radionuclides given below and their corresponding half-life periods. Which statement below is true? a. Phosphorous 28 decays taster and is the least stable nuclide. b. Phosphorous 28 decays faster and is the most stable nuclide. c. Phosphorous 32 decays faster and is the most stable nuclide. d. Phosphorous 32 decays faster and is the least stable nuclide. e. They both decay at the same rate but Phosphorous 28 is more stable.

Provided in the table below are two isotopes and their corresponding half-life periods. Which isotope decays the fastest and which isotope is the most stalve?a. They both decay at the same rate and Vanadium-50 is the most stable.b. Uranium-235 decays the fastest and Vanadium -50 is the most stable.c. Uranium-235 decays the fastest and is the most stable.d. Vanadium-50 decays the fastest and Uranium-235 is the most stable.e. Vanadium-50 decays the fastest and is the most stable.

The half-life of phosphorus-32 is 14.26 days. Calculate its decay constant.Express the decay constant numerically in inverse days.