Nuclear Half-Life Calculations

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Questions

• How do you calculate nuclear half life?
• Question #b61f8
• Question #406c5
• What is the half-life of a radioisotope if 1/16 of it remains undecayed after 26.4 days?
• If a radioactive Isotope has a half life of 30 days then how long will it take 1000 grams to decay to 120 grams?
• If the half life of an unstable element is 5000 years, what percentage of the parent material will be left after 10000 Years?
• How much material will be left if a radioactive isotope has a half life of 1.3 billion years in 3.9 billion years?
• Can you determine the annual decay rate of a certain radioactive isotope that has a half life of 231 years?
• If 100.0 g of a radioactive isotope that has a half life of 25 years, identify the amount of that isotope that will remain after 100 years?
• How many minutes will it take for an isotope that has a half life of 45 minutes to decay to 1/8th of its original amount?
• If a radioactive isotope has a half-life of 100 years. A sample of 40 grams of the isotope will have a mass of how many grams in 200 years?
• If a radioactive sample has half the radioactive atoms left after 20 years, what is its half-life?
• What The half-life of potassium-40 is about 1300 million years. After for half lives have passed, how much of the original sample will be left?
• When Iodine-131 has a half-life of 8.0 days. How many grams of an original 160 mg sample will remain after 40 days?
• How long will it take for 3/4 of the sample of 131 iodine that has half-life of 8.1 days?
• If the half-life of iodine-131 is 8 days, how much of a 5-g sample is left after 32 days?
• Radioactive iodine-131 has a half-life of eight days. The amount of a 200.0 gram sample left after 32 days would be?
• What is the rock's age? A rock contains one-fourth of its original amount of potassium-40 The half-life of potassium-40 is 1.3 billion years?
• How do you calculate the number of days required for 3/4 of a given amount of nuclide to decay if the half-life is 18 point 72 days?
• How does radioactive decay relate to radiometric dating?
• How can I calculate the rate of decay of a radioactive element?
• How can I calculate the half life of an isotope?
• How can I calculate the half life of an element?
• What is the half life equation?
• What is an example of a decay practice problem?
• What is decay?
• What are some examples of half-life calculations?
• What Carbon-14 has a half-life of nearly 6000 years. If one half-life (50 %) of the original carbon-14 is left in a material, how old is it?
• Question #59bcf
• Question #2ac43
• Question #2ac56
• Question #63c46
• Question #fca61
• Question #c4d7e
• Question #bbfad
• Question #2e0a3
• Question #027ec
• Question #cf933
• Phosphorus-32 has a half-life of 14.0 days. Starting with 8.00g of 32P, how many grams will remain after 70.0days ?
• Question #1991a
• Question #e121a
• Question #7fe9c
• Question #ab040
• Question #43a81
• The half-life of strontium-90 is 28 years. How long will it take a 44 mg sample to decay to a mass of 11 mg?
• Thorium-234 has a half-life of 24 days. if you started with 100 gram sample of thorium-234, how much would remain after 48 days?
• The half-life of plutonium-239 is 24,100 years. Of an original mass of 100g, how much plutonium-239 remains after 96,440 years?
• The half-life of cobalt—60 is 5.27 years. How many milligrams of cobalt-60 remain after 52.7 years if you start with 10.0 mg?
• How many milligrams of a 15.0 mg sample of radium-226 remain after 6396 years if the half-life of radium-226 is 1599 years?
• A radioactive element has a half-life of 5 years. If you leave a 2 g sample of this element under your chemistry desk for 15 years, what mass will remain undecayed?
• The activity of a sample of radioactive material is measured,and found to be 880 Bq. After 160 minutes the activity has fallen to 55 Bq. What is the half-life of Bq?
• Radon-220 has a half-life of 54 seconds. How much of a 20g sample of this gas would remain after 162 seconds?
• At the beginning of an experiment, a scientist has 372 grams of radioactive goo. After 135 minutes, her sample has decayed to 23.25 grams. What is the half-life of the goo in minutes?
• The half-life of the decay of radioactive cesium(134) has been reported to be 2.062 years. What fraction of the original radioactivity will remain after 67 months?
• A fossil fuel contains 70% of the carbon-14 it once had as a living creature. How would you use the half-life decay equation to determine when the creature died?
• A parchment fragment was discovered that had about 74% as much Carbon 14 radioactivity as does plant material on the earth today. How would you estimate the age of the parchment?
• Carbon-14 has a half-life of 5770 years. If a fossil is 23,080 years old and it has 3kg of Carbon-14, how much carbon-14 did it originally have?
• Protactinium-234 has a half life of 1.17 minutes. How long does it take for a 10 mg sample to decay to 2 mg?
• A patient is given #0.050# #mg# of technetium-99m, a radioactive isotope with a half-life of about #6.0# hours. How long until the radioactive isotope decays to #6.3 * 10^-3# #mg#?
• Question #46693
• Question #3890e
• Question #c035b
• Question #72e48
• Question #dd2af
• What fraction of a radioactive sample remains after three half-lives?
• The half-life of Iodine-131 is 8 days. What mass of I-131 remains from an 8.0g sample after 2 half-lives?
• How old is a mammoth's tusk if 25 percent of the original C-14 remains in the sample, if the half-life of C-14 is 5730 years?
• Question #95320
• The half-life of #""^131"I"# is 8.07 days. What fraction of a sample of #""^131"I"# remains after 24.21 days?
• The half-life of carbon-14 is 5700 years. What is the age to the nearest year of a sample in which 39% of the radioactive nuclei originally present have decayed?
• If the half life of uranium-235 is #7.04 * 10^8# y and 12.5 g of uranium-235 remain after #2.82 * 10^9# y, how much of the radioactive isotope was in the original sample?
• You have found a fossilized leg bone of some unknown mammal. Based on the size of the bone, you determine that it should have contained about 100 g of carbon-14 when the animal was alive. The bone now contains 12.5 g of carbon-14. How old is the bone?
• Lf gallium-68 has a half life of 68.3 minutes, how much of a 10.0mg sample is left after one half life? Two? Three?
• A sample of wood contains 12.5% of its original carbon-14. What is the estimated age of this sample?
• How many years are required for 28 mg of cesium-137 to decay to 3.5 mg of cesium-137?
• If the mass of a radioactive substance is 8 grams and it has a half life of 4 hours, how much mass remains after 8 hours?
• The half-life of radon-222 is 3.8 days. What was the original activity if it has an activity of 10 Bq after 7.6 days?
• What is the half-life of 20 g of a radioactive sample if 5 g remain after 8 minutes?
• A radioactive element has a half life of 2,000 years. If a sample of this element begins with a mass of 100 grams, how long would you have to wait for the mass to decrease to 25 grams?
• If 1250 counts of an originally 10,000 count radioactive sample are being emitted after one (24 hour) day, what is the half-life of the element?
• Phosphorous-32 has a half life of 14.3 days. A 30-count sample is stored for 114.4 days. How much radiation remains in the original sample?
• Question #bbcf9
• If a sample originally had 120 atoms of carbon-14, how many atoms will remain after 16,110 years?
• If you had a 100-gram sample of plutonium, how much would still remain in 43 years?
• The half-life of radon-222 is 3.82 days. If a sample of gas contains 4.38 #mug# of radon-222, how much will remain in the ample after 15.2 days?
• What is the fraction of a sample of carbon-14 left after 22,800 years if its half life is 5,700 years?
• Suppose the half life of element K is 20 minutes. If you have 200 g sample of K, how much of element K will be left after 60 minutes?
• What fraction of a given sample of a radioactive nuclide remains after four half-lives?
• Question #58689
• The half-life of cobalt-60 is 5.27 years. Approximately how much of a 199 g sample will remain after 20 years?
• Polonium-214 has a relatively short half life of 164 s. How many seconds would it take for 8.0 g of this isotope to decay to 0.25 g?
• Iodine-131 is a radioactive isotope with a half-life of 8 days. How many grams of a 64 g sample of iodine-131 will remain at the end of 24 days?
• The half-life for the radioactive decay of calcium-17 is 4.5 days. How many half-lives have elapsed after 18 days?
• If we start with 8000 atoms of radium-226, how much would remain after 3,200 years?
• How much grams of a substance will be left after 2 hours if its half life is 15 minutes?
• Question #e2e73
• Question #72f8f
• If actinium 227 has a half life of 21.77 years, how many years have gone by if actinium-227 undergoes 3 half-lives?
• In 5.49 seconds, 1.20 g of argon-35 decays to leave only .15 g. What is the half life of argon-35?
• If 100 g of Au-198 decays to 6.25 g in 10.8 days, what is the half-life of Au-198?
• The half-life of cobalt-60 is 5.26 years. If 50 g are left after 15.8 years, how many grams were in the original sample?
• The half-life of radon-222 is 3.8 days. How much of a 100 g sample is left after 15.2 days?
• The isotope chromium-51 has a half-life of 28 days. If the original sample had a mass of 28.0 grams, what mass of the chromium-51 sample remains after 84 days?
• Question #7e3ca
• A uranium-235 sample starts with 200 atoms, and 700 million years later, there are 100 atoms. What is the half-life of uranium-235?
• Sodium-24 has a half-life of 15.0 hours. Suppose you had a sample containing 0.010 moles of Na-24. How many hours would be required to reduce your sample to 6.25 x 10^-4 moles?
• The half life of radon-222 is 3.824 days. After what time will one fourth of a given amount of radon remain?
• You are given 500 grams of a substance with a half-life of 1.5 years. How much will remain after 15.0 years?
• How old is a fossil that has radioactively decayed through 4 half-lives of carbon-14?
• What mass of #""^(55) "Cr"# must be delivered in #"mg"# to a patient if the total drug transport time is #"12 hours"# and the minimum dosage needed is #"1.0 mg"#? The half-life is #"2 hours"#.
• Carbon-14 has a half-life of 5770 years. If a fossil is 23,080 years old and it has 3 Kg of Carbon-14, how much carbon-14 did it originally have?
• What does the 0.693 represent in the equation of half life (t1/2 = 9.693/k) ?
• What is the half life formula?
• The half-life of cobalt-60 is 5.2 years. Find the time it would take for a sample of 0.5 grams to decay to 0.1 gram?
• The half-life of cobalt-60 is 5.2 years. Find the time it would take for a sample of 0.5 grams to decay to 0.1 gram?
• What amount of plutonuim would be left after 5000 years if you initially have 14 kilo- grams? The half-life of plutonium 240 is 6500 years.
• A radioactive substance has a half-life of 125 years - if there were originally 80 radioactive milligrams 50 years ago, how much is still radioactive today?
• If you have 100mg of a drug with a half-life of 4 hours, how long will it take to totally eliminate it from the body?
• The half-life for radioactive decay (a first-order process) of plutonium-239 is 24,000 years. How many years would it take for one mole of this radioactive material to decay so that just one atom remains?
• The mass of cobalt-60 in a sample is found to have decreased from 0.800g to 0.200g in a period of 10.5 years. From this information, what is the half-life of cobalt?
• Carbon-14 has a half life of 5730 years. If a shell is found and has 52% of its original Carbon-14, how old is it?
• Question #0ff3e
• The water in a lake contains a certain amount of tritium #sf(""^3T)#. The water is used to make wine and whisky. Given that the half - life of tritium is 12.3 years can you answer the following ?
• What percentage of strontium-90 remains in a sample after two first-order half-lives have passed?
• How much Cu-64 (half-life about 12 hours) would remain from a 2 mg sample after 12 hours?
• Question #bb66f
• How long would it take for fifteen-sixteenths of a sample of radon-222 to decay?
• Carbon-14 has a half-life of 5,730 years. How long will it take for 112.5 g of a 120.0 g sample to decay radioactively?
• The half-life of a certain substance is 3.6 days. How long will it take for 20 g of the substance to decay to 7 g?
• If a 12.0-g sample of radon-222 decays so that after 19 days only 0.375 g remains, what is the half-life of radon-222?
• If we start with 1 mg of strontium, 0.953 mg will remain after 2.0 years. What is the half life of strontium-90?
• Question #272dc
• The half-life of bromine-74 is 25 min. How much of a 6.0 mg sample is still active after 75 min?
• Krypton-79 has a half-life of 35 h. How many half-lives have passed after 2 days?
• What is the half-life of a first-order reaction with a rate constant of #7.80xx10^-4 s^(-1)#?
• What is the half-life when the initial concentration is 0.51 M?
• A sample of U-238 initially contained #1.3x10^18# atoms when the universe was formed 13.8 billion years ago, how many U-238 atoms will it contain today?
• The half life of bromine-73 is 20 min. How much 10 mg sample is still active after 60 min?
• Question #5e9e6
• A radioisotope has a five-year half life. After a given amount decays for 25 years, what fraction of the original isotope is left?
• A sample of a radioactive isotope is found to have lost 39.9% of its original activity after 8.57 days. What is the decay constant of this isotope?
• A sample of rock is found to contain 100 grams ion a parent isotope. How many grams of the parent isotope will remain after two half lives?
• The half-life of Iodine-131 is approximately 8 days. What is the amount of Iodine-131 left from a 35 gram sample after 32 days?
• Living matter has a carbon-14 activity of about 16 counts/min per gram of carbon. What is the age of an artifact for of which the carbon-14 activity is 8 counts/min per gram carbon?
• Mercury-197 is used for kidney scans and has a half-life of 3 days. If the 32 grams of mercury-197 is ordered, but takes 15 days to arrive, how much would arrive in the shipment?
• Technetium 99 is used for brain scans. If a laboratory receives a shipment of 200 g of this isotope, how much will remain after 24 hours? The half life of Technetium 99 is 6 hours.
• Technetium 99 is used for brain scans. If a laboratory receives a shipment of 178 g of this isotope, how much will remain after 15 hours? The half life of Technetium 99 is 6 hours.
• Uranium-235 has a half-life of 700 million years. How long does it take a 100-gram sample of Uranium-235 to decay to a mass of 50 grams?
• Question #80545
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• Question #f25a9
• Question #21f9a
• How many half life would it take for a sample of corbon-14 to be reduced to 1/32 of its original mass?
• The half-life of cesium-137 is 30.2 years. If the initial mass of a sample of cesium-137 is 1.00 g, how much will remain after 30.2 years?
• A bone was found to be approximately 24000 years old. The current amount of carbon-14 in the bone was 5.000 atoms. How many atoms must the bone have had originaly, assuming that the half-life of carbon-14 is approximately 6000 years?
• Starting with 189 grams of uranium-238, after one half life has gone by, how many grams of uranium-238 will remain?
• Barium-131 is a radioactive isotope of the element barium used gastrointestinal tract scans in doctors offices. Barium-131 has a half-life of 10 days. lf a patient drinks 3.9 grams of barium-131 how much of the isotope will be left after 1 days?
• The half-life of P-32 is 14.30 days. How many milligrams of a 20.00 mg sample of P-32 will remain after 85.80 days?
• 4. Suppose a laboratory has a 26 g sample of polonium 210. The half-life of Polonium 210 about 138 days. How many half-lives of polonium 210 occur in 276 days? How much polonium 210 is in the sample 276 days later?
• The half life of a radioactive isotope is 350 years. How do you find the amount remaining after 800 years, if the initial amount is 64 grams?
• After two half lives, what fraction of a radioactive sample has decayed?
• If a substance has a half life of one million years, how much of its will be left after three million years? After four million years?
• An old ax handle is found to have one-half as much carbon-14 as a sample of bark taken from a young tree. How old is the ax handle?
• The half-life of an element is #5.8 x 10^11#. How long does it take a sample of the element to decay to #2/5# its original mass?
• What is the half-life of a radioactive isotope if a 500.0 g sample decays to 62.5 g in 24.3 hours?
• Phosporous-32 is a radioisotope used in molecular biology After 44 days, 17% of the sample remains. How do you calculate the half-life?
• An original sample of K-40 has a mass of 25.00 grams. After #3.9 xx 10^9# years, 3.125 grams of the original sample remains unchanged. What is the half-life of K-40?
• Question #370a1
• If half of a radioactive sample decays after 1 day, will the other half decay after 1 additional day? Why or why not?
• Question #f85fc
• Question #bf230
• The half-life of cesium-137 is 30 years. Suppose we have a 120-mg sample. Find the mass that remains after #t# years. How much of the sample remains after 90 years? After how long will only 1 mg remain?
• The half life of a specific radionuclide is 8 days. How much of an 80 mg sample will be left after 24 days?
• If a scientist purifies 10 gram of radium-226, how many years must pass before only 0.50 gram of the original radium-226 sample remains unchanged?
• If 12.5 grams of the original sample of cesium-137 remained after 90.6 years, what was the mass of the original sample?
• Why is N-16 is a poor choice for radioactive dating of a bone?
• A rock contains 0.688 mg of #"^206Pb# of every 1000 mg of #"^238U#. How do you calculate the age of the rock?
• Actinium-227 has a half life of #8 x 10^3# days, decaying by a #alpha#-emission. Suppose that the helium gas originating from the alpha particles were collected. What volume of helium at 25°C and 748 mmHg could be obtained from 1.00 g after 100 years?
• Gold-198 has a half-life of 2.7 days. How much of a 96g sample of gold-198 will be left after 8.1 days?
• Co-60 is a beta emitter with a half-life of 5.3 years. Approximately what fraction of Co–60 atoms will remain in a particular sample after 26.5 years?
• Question #e627c
• Given the following chart, what will the rock contain after 40.000 years or 2 half-lives?
• A rock is found contains uranium-238 and also lead-206. Scientist analyze the rock for these two elements and find that the total mass of uranium in the rock is 2.40 g, while the amount of lead is 1.11 g. How old is this rock?
• Question #a4462
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• Question #116c1
• Question #d5cfe
• The population of a herd of sheep declines exponentially. If it takes 3 years for 15% to decline then how long will it take for half the population to decrease ?
• Curium has a half life of 1.5 hours, how much of a 1000g sample remains after: 1.5 hrs? 3hrs? 4.5 hrs? 6hrs?
• Question #b3120
• How do you find the half life of uranium-235? I tried to do 235 / 2 = 117.5 but that is wrong please help
• Charcoal used to make prehistoric drawings on cave walls in France was analyzed. The results were 4 mg carbon-14 (parent isotope) and 60 mg nitrogen (daughter isotope). The half-life of carbon-14 is 5,730 years. How old are the cave drawings?
• If a sample of organic material contains 1/8 of the radioactive #"^14C# than a modern day sample and the half-life for #"^14C# is 5,730 years, approximately how old is the order sample of organic material?
• Titanium-44 is radioactive isotope such that every 63 years, its mass decreases by half. For a sample of titanium-44 with an initial mass of 100 grams, what is a function that will give the mass of the sample remaining after any amount of time?
• An element with mass 130 grams decays by 22% per minute. How much of the the element is remaining after 7 minutes, to the nearest 10th of a gram?
• The half-life or a radioactive isotope is the time takes tor a quantity for the isotope to be reduced to half its initial mass. Starting with 150 grams ot a radioactive isotope, how much will be left atter 6 half-lives?
• Question #cc5db
• A fossil is found to have #1/32# of its carbon- 14 remaining. How old is the fossil?
• A substance has a half-life of 3 years. If 2000 grams are present initially, how much will remain after 1.5 years?
• Question #3594d
• Question #70676
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• Question #24d75
• Iodine-131, #t_(1/2)# = 8.0 days, is used in treatment of thyroid gland diseases. If a sample of iodine-131 initially emits #9.95 x 10^18 beta# particles per day, how long will it take for the activity to drop to #6.22 x 10^17 beta# particles per day?
• Carbon dating is accurate for organic matter up to how old?
• One uranium atom has a mass of #3.95 x 10^-22# grams. How would you work out an estimate for the number of uranium atoms in 1kg of uranium?
• A sample of wood that originally contained 100 grams ofcarbon-14 now contains only 25 grams of Carbon-14. Approximately how many years ago was this sample part of a living tree?
• A sample is dated using uranium-235 (half-life 704,000,000 years) and it has 4 of the original amount of uranium. How old is the sample?
• Element X has a half-life of 6000 years. If you a fossil and find only 12.5% of the original amount of element X, what would the age of the specimen be?
• Question #db7d8
• Question #cf178
• Question #cff1c
• Question #18b2d
• If it takes #"3 min"# for #40%# of sucrose to dissolve in a certain amount of water, how long does it take for all but #10%# of the sugar to dissolve?
• Question #40235
• Thorium-234 has a half life of 24 days. If you started with a 100-g sample of thorium-234 how much would remain after 48 days?
• Suppose a laboratory has a 31 g sample of polonium-210. The half-life of polonium-210 is about 138 days. How many half lives of polonium occur in 966 days? How much polonium is in the sample 966 days later?
• Question #27f24
• An animal dies in the forest. How long will it be until only #7/8# of the original amount of Carbon 14 remains?
• Question #076dd
• The half life of #"^131I# is 8.021 days. What fraction of a sample of #"^131I# remains after 24.063 days?
• If 1/8 of an original sample of krypton-74 remains unchanged atter 34.5 minutes, what is the half life of krypton-74?
• The radioisotope radon-222 has a half life of 3.8 days. How much of a 73.9 g sample of radon-222 would be left after approximately 23 days?
• You have 7,232 grams of a radioactive kind of uranium. How much will be left after 56 hours if its half-life is 14 hours?
• Question #5ef03
• Question #97af1
• Question #444dd
• Uranium-238 that crystallized at the same tim Earth formed has undergone approximately how many half-lives of radioactive decay?
• Radioactive decay of #""^40K# atoms in an igneous rock has resulted in a ratio of 25 percent #""^40K# atoms to 75 percent #""^40Ar# and #""^40Ca# atoms. How many years old is this rock?
• Curium-243 has a half-life of 285 days. In a sample of 5.6 grams of curium-243. how many grams will remain after 12 days?
• Question #d1146
• The half life strontium-90 is 28.8 years. How much of a 325 gram sample is remaining after 4 of half lives? How old is the sample?
• How many half-lives have elapsed when 25% of the parent nuclide is left?
• Krypton-79 mg has a half-life of 35 h. How many half-lives have passed after 105 h?
• Question #ea645
• #Q(t) = Q_(o)e^(-kt)# may be used to model radioactive decay. #Q# represents the quantity remaining after years; #k# is the decay constant, 0.00011. How long, in years, will it take for a quantity of plutonium-240 to decay to 25% of its original amount?
• Question #8336d
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• Question #568a2
• Question #39370
• Question #2b3b7
• Question #9dcb1
• Question #338a0
• Question #611ac
• If a nucleus has #44# positively charged, massive particles, and #62# neutral, massive particles, what is the nucleus, and how do we represent it?
• Question #36005
• A sample of rock is known to be #4.2xx10^(9)# years old. It contains 1.235 g of U 238. What is the mass of Pb 206 present in the sample assuming all of it originated from the decay of U 238 which has a half life of #4.489xx10^9# years ?
• Question #188b6
• Question #dbed0
• Question #d1e8d
• Iron-59 has a half-life of 45.1 days. How old is an iron nail if the Fe-59 content is 25% that of a new sample of iron? Show all calculations leading to a solution.
• A radioactive nucleus alpha decays to yield a sodium-24 nucleus in 14.8 hours. What was the identity of the original nucleus? Show the nuclear equation that leads you to this answer.
• A sample of rock is known to contain the isotopes U 238 and Pb 206 in the mass ratio of 2:1. What is the age of the sample assuming all the Pb 206 has originated from the decay of U 238 ?The half - life of U 238 is #4.468xx10^9# years.
• Question #e0dc9
• Question #e7a7d
• What fraction of the amount of carbon-14 that was the mammoth's tooth when it died is left after five half-lives?
• Suppose you find a rock originally made of potassium-40, half of which decays into argon-40 every 1.25 billion years. You open the rock and find 31 atoms of argon-40 for every atom of potassium-40. How long ago did the rock form?
• Question #b599d
• Question #7bdb7
• The half-life of cobalt-60 is 5.3 years. How many years will it take for 1/4 of the original amount of coblat-60 to remain?
• Question #7f902
• Question #74008
• Radioactive element X has a half-life of 30 days. A rock sample contains 4 grams element X when it forms. How many half-lives will have elapsed in 90 days? How much of the original amount of X will be unchanged after 90 days?
• An archaeologist unearths the remains of a wooden box, analyzes for the carbon-14 content, and finds that about 93.75% of the carbon-14 initially present has decayed. The half-life of carbon-14 is 5600 years. How old is the box?
• A first-order reaction has a hall-life of 21.3s. How long does it take for the concentration of the reactant in the reaction to fall to one-eighth of its initial value?
• Question #7edac
• Question #1f1d8
• The half-life of a first-order reaction is 1.5 hours. How much time is needed for 94% of the reactant to change to product?
• Question #e3336
• Question #d4494
• The half life of a radioactive element is 30 seconds. In what period of time would the activity of the sample be reduced to one - sixteenth of the original activity?
• How many half-lives will it take to reach 6.25% of its original concentration?
• Half life of potassium-40,is approximately 1.25 billion years.what will be the fraction of radioactivity left after 5 billion years?