A radioactive substance has a decay rate of 4% per hour. If 1000 grams of the substance are present initially, how many grams remain after 5 hours?

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 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: 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 radioactive material decays at a rate proportional to its amount. If the material has a life of 30…

A: This question is based on application of differential equation.

Q: A sample of a newly discovered element, West Virginium, has a half-life of 425 years. How long will…

A: Given half life of element is 425 years t1/2. Initial weight A0 is 803 mg and after decay is 401.5…

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 radioactive substance has a half-life of 29 years. What percent remains 80 years after being to…

A: We will find the remains after 80 years in percentage.

Q: Given that the half-life of radium is 1690 years, how much in milligrams will remain of one gram of…

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

A:

Q: During a preliminary survey of an asteroid, chemical analysis indicated that a certain radioactive…

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Q: If half a certain amount of radium decays in 1600 years. What percentage of the original amount will…

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Q: An element with mass 970 grams decays by 27.7% per minute. How much of the element is remaining…

A: Given that, The mass of the element is 970 grams, which decays by 27.7% per minute. To find: How…

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: 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: An initial population of 8,000 decays for two years until the population is 500. By what percentage…

A: Given-  An initial population of 8,000 decays for two years until the population is 500. To…

Q: The population of minnows in the lagoon is 5,400, but the population will decay exponentially. If…

A: The formula for the exponential decay model is, y=C1-rt Here, y is the final amount C is the initial…

Q: An isotope of cesium has a half life of 29 years. If 1300 grams of cesium disintegrates over a…

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

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Q: The half life of a certain isotope is 8.5 hours. If we have a sample of 10 ounces of that isotope,…

A: Consider the following information: Half life periodt12=8.5 hours Decay constantλ=ln2t12=ln28.5…

Q: A 50-mg sample of a radioactive substance decays to34 mg after 30 days. How long will it take for…

A: Given: A 50 - mg sample of a radioactive substance decays to 34 mg after 30 days. To find: The time…

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: 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 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: 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 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…

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

A: There is a decay of element at the rate of 28.6% per minute. Initially the mass of element given is…

Q: Of an initial amount of 4000 g of lead-210, how much will remain in 190 years? Lead-210 decays at a…

A: Here initial amount A0=4000g Decaying rate λ= 3.15% = 0.0315 Let amount remains in 190 years= A(t)

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: If18 g of a radioactive substance are present initially and 4yr later only 9g​remain, how much of…

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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 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: 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: An

A: Given,element with mass = 510 gramsdecay rate = 26.3% per minuteour aim is to find how much of the…

Q: Researchers recorded that a certain bacteria population declined from 100,000 to 100 in 24 hours. At…

A: We have to find number of bacteria in 8 hours into the experiment where researchers recorded that a…

Q: Strontium-90 is a radioactive isotope with a half-life of 29 years. Strontium-90 is a major…

A: The half-life , T12 , is calculated using the formula, T12=ln 2λ , where, λ is the decay constant.…

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: 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 element with mass 310 grams decays by 8.9% per minute. How much of the element is remaining after…

A: Given   mass = 310 gm  Rate = 8.9 %  Time = 19 min

Q: Radioactive radium has a half-life of approximately 1599 years. What percent of a given amount…

A: A(t)=A012thh is the half lifeA(t) is the amount after t years.A0 is the initial value.

Q: The half-life of radioactive strontium-90 is approximately 27 years. In 1963, radioactive…

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

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Q: A 50-mg sample of a radioactive substance decays to 34 mg after 30 days. How long will it take for…

A: The radioactive decay is modelled using the equation: N(t)=N0e-kt, where N0 is the initial amount…

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: 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.