The radioactive isotope of lead Pb-209, decays at a rate proportional to the amount present at any time and has a half-life of 3.3 hours. If 1 gram of lead is present initially, how long will it take for 80% of lead to decay.

Q: The half-life of strontium-90 is 28 years. How long will it take a 56 mg sample to decay to a mass…

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Q: Of an initial amount of 6000 g of lead-210, how much will remain in 110 years? Lead-210 decays at a…

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Q: The half-life of radium-226 is approximately 1620 years. How much time is necessary for a sample…

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Q: If you start with 65 milligrams of Chromium 51, used to track red blood cells, which has a half-life…

A: N(t)=N0e-tln2h N0=Initial amountt=decay timeh=length of half life Initial amount= N0=65 milligrams…

Q: How much of a 500g sample of potassium-42 is left after 62 hours if the half life of potassium-42 is…

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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: The half-life of the plutonium isotope is 24,360 years. If 10 g of plutonium is released into the…

A: It is given that the half-life of the plutonium isotope is 24,360 years. Use formula, an exponential…

Q: The half-life of substance X is 3.5 years.  How long will it take for a 96.0 mg sample of substance…

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Q: After the release of radioactive material into the atmosphere from a nuclear power plant in a…

A: Given that  To find the how long did the farmers need to wait to use this hay

Q: After 2250 years, 25% of a radioactive material remains. If the rate of decay of the material is…

A: Half-life = 0.693/Decay constant(lambda)

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: Of an initial amount of 5000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

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Q: Of an initial amount of 9000 g of lead-210, how much will remain in 120 years? Lead-210 decays at a…

A: Apply the formula  P(t)=Po(1-r)t where, Po is the initial quantity r is the rate and t is the time.…

Q: Most smoke detectors contain a tiny amount of Americium-241, which is an artificially produced…

A: Assuming that the radioactive decay follows exponential distribution, the quantity of substance…

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: 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: The half-life of the plutonium isotope is 24,360 years. If 10 g of plutonium is released into the…

A: Half life of the plutonium isotope is 24,360 years. If 10g of plutonium is released into the…

Q: The half-life of plutonium-241 is approximately 13 years. How much time is necessary for a sample…

A: The exponential formula for decay is given as: A=A0e-λt               ⋯2, where A is future amount,…

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: 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: If 275 mg of a radioactive element decays to 200 mg in 48 hours, what is its half-life?

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Q: A tumor is injected with 0.9 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: 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: The half-life of strontium-90 is 28 years. How many years will it take a 56 mg sample to decay to a…

A: Given : Half -life of strontium-90 is 28 years . T1/2 = 28 years

Q: The half -life of carbon-14 is 5,730 years. Suppose a fossil is found with 20% as much of its…

A: Given that the half-life of carbon-14 is 5,730 years. So, h=half life=5730 Let the initial amount=P=…

Q: A certain radioactive substance decomposes at a rate proportional to the amount present. Of the 1000…

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Q: A radioactive material decays at a rate proportional to its amount. If the material has a half-life…

A: model is  A=A0ektfor half-life put A=A02thenA02=A0ektsolving for t, we get k=-ln(2)t

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: Of an initial amount of 4000 g of lead-210, how much will remain in 130 years? Lead-210 decays at a…

A: Find much much will remain

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: A sample of a radioactive substance decayed to 10% of its original amount after 30 years. What is…

A: Given After 30 years substance decayed to 10 % of its original amount

Q: A certain radioactive substance has a half-life of 38 hours. Find how long it takes for 90% of the…

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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: The​ half-life of​ carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree…

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Q: Thorium-227 has a half-life of 18.4 days. How many days will a 100mg sample take to decay to 12.5mg?

A: Here, we need to find how many days will a 100mg sample of Thorium-227 take to decay to 12.5mg.

Q: A 50 mg sample of thorium-233 decays to 44 mg after 4 min. a) Determine the half-life of…

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Q: An unknown radioactive element decays into non-radioactive substances.  In 660 days the…

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Q: An element with mass 490 grams decays 28.6% per minute. How much of the element is remaining after…

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Q: A tumor is injected with 0.7 grams of Iodine-125, which has a decay rate of 1.15% per day. To the…

A: The exponential function A = P * (1 - r)t  where A is the final amount and P is your inital amount.…

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: A radioactive substance is known to have a half-life of 78 years. Calculate the number of years it…

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Q: After 15 years, one fourth of the initial mass of radioactive substance has decayed. a) Find the…

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Q: If 250 mg of a radioactive element decays to 200 mg in 48 hours, find the half-life of the element.

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

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Q: Element X decays radioactively with a half life of 8 minutes.If there are 980 grams of Element X,…

A: We have to find the time

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.