Most smoke detectors contain a tiny amount of Americium-241, which is an artificially produced radioactive element having a half-life of 432 years. If a smoke detector contains 2.5 micro- grams of Am-241 when it is new, how much will remain when it is 100 years old?

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

A:

Q: Suppose a small quantity of radon gas, which has a half-life of 3.8 days, is accidentally released…

A: half life problem

Q: In the early 1960s, radioactive strontium-90 was released during atmospheric testing of nuclear…

A: the radioactive decay is a continuous process. Therefore, A=A0ert where A is the amount remaining,…

Q: A certain radioactive substance has a half-life of 38 hr. Find how long it takes for 80% of the…

A: Given that: Half life, t1/2=38 hr

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

A: The radioactive element​ carbon-14 has a​ half-life of 5750 years, then the decay constant λ by…

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: You have 10 ounces of a radioactive substance with a half-life of 5 hours. How long will it be until…

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

A: Given that the​ half-life of​ carbon-14 is 5600 years and if a piece of charcoal made from the wood…

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

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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: The half-life of strontium-90 is 28 years. How long will it take a 40 mg sample to decay to a mass…

A:

Q: A sample of a newly discovered element, West Virginium, has a half-life of 170 years. How long will…

A: We have to find the time required.

Q: The half-life of Uranium-238 is approximately 4.5(10°) years. How much of a 10 kilogram block of U–…

A:

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

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

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

A:

Q: A sample of a newly discovered element, West Virginium, has a half-life of 295 years. How long will…

A: We have to find out t

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: If 525 mg of a radioactive element decays to 450 mg in 48 hours, what is its half-life?

A: we are using model for radioactive decayN=N0e-λtwhereN0=initial amountN=The amount test of a…

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: An isotope Of thorium has a half-life Of 18.4 days. To the nearest day, how long will it be until…

A: Given half life = 18.4 days

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

A:

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: 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…

A:

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

A:

Q: A certain radioactive isotope has a half-life of approximately 1750 years. How many years to the…

A: Consider the amount is, A=Pert here, A is the isotope, P is the initial amount and r is the…

Q: A tumor is injected with 0.9 grams of Iodine-125, which has a decay rate of 1.15% per day. To the…

A:

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

A:

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

A:

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

A:

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

A:

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

A:

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: Suppose that we initially have 500 mg of a radio-active substance as sample. After a year, the…

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

A:

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 radioactive substance has a half-life of 25 years. If 640 grams of the substance are present…

A:

Q: If 12 g of a radioactive substance are present initially and 8 yr later only 6 g​ remain, how much…

A:

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

A:

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: A radioactive substance has a half-life of 4 hours. How much of it is left after 12 hours?

A: Since, a radioactive substance has a half-life of 4 hours.Our aim is to calculate the amount of…

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

A:

Q: he radioactive isotope gallium 67 has a biological half-life of 36 hours. If re start with 100…

A:

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

A:

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.