Radioactive cesium-137 has a half-life of 30.17 years. How much of an initial amount of 1,000 kilograms of cesium-137 will remain after 100 years?

Q: Radiocarbon C14 has a half-life of 5730 years. How many years will it take for 26%of a sample of C14…

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Q: The isotope cesium-137 has a half-life of 29.75 years. How long will it take a 100 gram sample of…

A: To determine the time taken for 100 gram sample of cesium-137 to decay to 75 grams.

Q: Cobalt-60 has a half-life of 5.24 years. (a) Find the mass that remains from a 100-mg sample after…

A: t=Duration of half life=5.24 years k=Constant C=Mass of Cobalt=100 mg…

Q: The half-life of Radium-226 is 10 years. How much of an initial 138 g sample will remain after 49…

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Q: Assume that radium disintegrates/decomposes at a rate proportional to the amount present. If 100 mg…

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Q: A scientist begins with 225 grams of a radioactive substance. After 300 minutes, the sample has…

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Q: Radium-221 has a half-life of 30 sec. How long will it take for 83% of a sample to decay?

A: If Ao is initial amount of Radium-221. substance, h is half-life of substance and t is elapsed time.…

Q: Yttirum-90 has a half-life of 64.10 hours. Given an initial mass of 622 grams of the sample, how…

A: Given information Half life t12=64.10 hours And the initial mass m0=622 grams We have to find the…

Q: Yttirum-90 has a half-life of 64.10 hours. Given an initial mass of 659 grams of the sample, how…

A: Half-life is the time required for a quantity to reduce to half of its initial value. The term is…

Q: of a radiooctive substonce decayed to 93.5% of its original sample amount after oyear What is the…

A: we need find half life substance k=? and t=?

Q: The half-life of radium in a piece of lead is 1600 years. What percentage of the original amount of…

A: Given that, the half-life of radium in a piece of lead is 1600 years. Note that, the formula for…

Q: What is the half-life of a radioactive substance if it takes 5 years for one-third of the material…

A: We have to find half life period

Q: The half-life of Cesium-137 is 30.7 years. How long will 200 grams of Cesium-137 take to decay to…

A: Given data The half-life of the cesium-137 is t1/2 = 30.7 years. The initial amount of the…

Q: Suppose a nuclear accident releases 50 kilograms of the element Cesium 137. If the half life of…

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Q: Yttirum-90 has a half-life of 64.10 hours. Given an initial mass of 551 grams of the sample, how…

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Q: The half life of a certain isotope is 6.13 hours. If we have a sample of 5.0 ounces of that isotope,…

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Q: Radioactive radium has a half-life of 1899 years. If 20g of the substance are present initially,…

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Q: Nobelium is a radioactive isotope that has 25 seconds half-life. How long will it take for Nobelium…

A: The formula to calculate the amount of radioactive isotope is N=Noe-λt where N is the rest amount No…

Q: Strontium-90 has a half-life of 29 years. If there are 400 grams of strontium initially, how much,…

A: Strontium-90 has a half-life of 29 years, there are 400 grams of strontium initially.

Q: Cobalt-60 has a half-life of 5.24 years. a. Find the mass that remains from a 100-mg sample after 20…

A: (a) Consider the mass remains from m0 mg sample after n years as m(t). The exponential equation can…

Q: if 8 g of a radioactive substance are present initially and 4 yr later only 4 g remain, how much of…

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Q: The half-life of plutonium-241 is approximately 13 years. How much of a sample weighing 4 g will…

A: The half-life of plutonium-241 is 13 years. We have to find how much sample of 4 g will remain after…

Q: Suppose you have 100g of Titanium-44, which has a half-life of 63 years. After how long will only 1g…

A: Initial amount=P=100  Half life= H= 63 years  Final amount= A= 1  Time= t years Using the half-life…

Q: An isotope has a half-life of 98 years. How much of a 16-gram sample is left after 150 years?

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Q: A tumor is injected with 0.4 grams of Iodine-125, which has a decay rate of 1.15% per day. To the…

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Q: The half-life of Radium-226 is 14 years. How much of an initial 143 g sample will remain after 43…

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Q: 40 grams of radioactive material decays to 35 grams in 20 years. Find the half-life.

A: In this question we need to find the half life of the given radioactive material

Q: A scientist begins with 450 grams of a radioactive substance. After 55 minutes, the sample has…

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Q: Of an initial amount of 8000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

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Q: How many half lives must have passed for an isotope with a half life of 10 years to decay from 1600…

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Q: The isotope cesium-137 has a half-life of 29.75 years. How long will it take a 100 gram sample of…

A: Half life of isotope  cesium-137 = 29.75 years. The decay equation of cesium-137 is given by Let…

Q: Radon-222 decays at a continuous rate of 17.3% per day. How much will 250 mg of Radon-222 decay to…

A: Radon-222, a noble gas resulting from the decay of naturally occurring uranium-238, is the first…

Q: Assume a substance has a half-life of 11 years and the initial amount is 133 grams.How much remains…

A: The amount left after t years can be calculated as

Q: Assume a substance has a half-life of 11 years and the initial amount is 133 grams.How long will it…

A: If A0 is initial amount present and T is half -life of the substance. Then the amount of substance…

Q: The radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that a…

A: The half life is 5750 years. Amount of carbon-14 lost is 28%.

Q: Radium has a weight of 1.5 and a half life of 6 years. What is its weight after 3 years?

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Q: Strontium-90 has a half-life of 25 years. How many years would it take 10 grams of strontium-90 to…

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Q: Suppose a radioactive substance has a half-life of 1000 years. What fraction will be leftafter 1000…

A: Given that the half life is 1000 years. This means 1/2 of the the original amount is left after 1000…

Q: A particular isotope has a half-life of 1 minutes.  If you start with 1 gram of this isotope, how…

A: To determine: A particular isotope has a half-life of 1 minutes.  If you start with 1 gram of this…

Q: Radioactive Radium Radium-221 has a half-life of 30 s. How long will it take for 95% of a sample to…

A: For decay of radioactive element                 Half life = ln 2decay constant         t12  = ln 2λ…

Q: Thorium -227 has a half life of 18.4 days. How many days will a 100mg sample take to decay to…

A: We know that, N(t)= N(0)*(1/2)t/(t1/2) N(t) = quantity of the substance remaining N(0) = initial…

Q: A sample of radium has a weight of 1.5mg and a half-life of approximately 6 years how much of the…

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Q: After 25 years, 60% of a radioactive substance still remains in a 20 gram sample. What is the…

A: Half life of a radio active material is the time required to reduce the initial quantity to its…

Q: The half-life of a radioactive material is about 34.2 years. How much of the material is left after…

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Q: The half-life of carbon-14 is 5730 years. How long does it take for 2.1 grams of carbon-14 to be…

A: A(t)=A0(1/2)t/h h is the half life A0 is the initial value

Q: 2. A radioactive material loses 25% of its mass in 10 minutes. What is its half-life?

A: Let No be the initial mass, N be remainingmass.  Then  N= No - 25100 No = No - No4=34NoHence    t…

Q: Of an initial amount of 7000 g of lead-210, how much will remain in 180 years? Lead-210 decays at a…

A: Given that: Initial amount of lead, P0=7000gRate of decay, k=3.15%per year.

Q: The half-life of Cobalt-60 is 14 years. How much of an initial 107 g sample will remain after 27…

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Q: Yttirum-90 has a half-life of 64.10 hours. Given an initial mass of 750 grams of the sample, how…

A: See the detailed solution below.

Q: A certain radioactive substance has a half-life of 38 hour. Find how long (in hours) it takes for…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.