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

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 y
b) 12.1 y
c) 11.5 y
d) 2.59 y
e) 5.25 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

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

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

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?

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 is left in the body after 54 days?

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 until the radioactive isotope decays to 6.3 times 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?

A fossil is found to have a 14C level of 77.0% compared to living organisms. How old is the fossil?

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.

32P is a radioactive isotope with a half-life of 14.3 days. If you currently have 45.9 g of 32P, how much 32P was present 2.00 days ago?

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.

The rate law for the rearrangement of CH3NC to CH3CN at 800 K is Rate = (1300 s-1) [CH3NC]. What is the half-life for this reaction? a. 1.9 x 10-3 s b. 1920 s c. 5.33 x 10-4 s d. 520 s

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?

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 of 206Pb per 1.260 g of 236U in the rock? The half-life of 236U is fv2 = 4.47 x 109 years.

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?

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.

Barium-122 has a half-life of 2 minutes. You just obtained a sample weighing 10.0 grams. If takes 10 minutes to set up the experiment in which barium-122 will be used. How many grams of barium-122 will be left when you begin the experiment?a. 0.313 g remainb. 0.625 g remainc. 0.00 g remaind. 50.0 g remaine. 2.00 g remain

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.

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.