When time is measured in days, the decay constant for a particular radioactive isotope is 0.14. Determine the time required for a confined sample of the isotope to fall to 40% of its original value.

Q: Determine whether the following statement is true or false, and explain why. The half-life of a…

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Q: 100mg sample of tritium-3 decayed to 94.5mg after a year. (i) What is the half-life of tritium-3?…

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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: 6. The radioactive isotope of lead, PB-209, decays at a rate proportional to the amount present at…

A: Let's find time to take 90% of the lead to decay.

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: 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: When time is measured in​ days, the decay constant for a particular radioactive isotope is 0.16.…

A: The equation for radioactive decay is N(t)=N0(e-λt), where N(t) is the new amount of isotope , N0is…

Q: The decay constant for the radioactive element strontium 90 is l = .0244, where time is measured in…

A: Definition used -                            Decay equation -…

Q: A sample of tritium-3 decayed to 94.5% of its originalamount after a year.(a) What is the half-life…

A: A sample of tritium-3 decayed to 94.5% of its original amount after a year. We have to find (a) What…

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

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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: 4.) The half-life of strontium-90 is 28 years. Find the rate of decay. How long will it take a 50 mg…

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Q: A certain substance decays so that each year 92% of the previous year's material is still present.…

A: A substance decay such that each year 92% of the previous year's material still remains. So, 8% of…

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: The decay constant for carbon-14 is 0.00012, with time measured in years. A piece of papyrus…

A: Decay of any radio active substance follow first kinetics and the equation of first order kinetics…

Q: How long does it take for 90% of a given quantity of the radioactive element cobalt-60 to decay,…

A: Radioactive element decay rate.

Q: Element X is a radioactive isotope such that every 70 years, its mass decreases by half. Given that…

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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 plutonium-241 is 13 years.  What is the decay constant?  Use the approximation…

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Q: Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that…

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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: 6. Determine the initial amount of radioactive substance if after 22 years, the remaining…

A: To find the initial amount of radioactive substance, decay rate and half-life of the substance.

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 radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the…

A: we have to determine time before the region is again habitable

Q: A radioactive substance has a half life of 175 years. Find the decay constant, r, for this…

A: A radioactive substance has a half life of 175 years

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: Suppose the half-life of a certain radioactive substance is 20 days and that there are5 grams…

A: Given that, The half-life of a certain radioactive substance is 20 days and that there are 5 grams…

Q: Element X is a radioactive isotope such that every 16 years, its mass decreases by half. Given that…

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Q: A certain element decays at a rate of .000163/year. Of a piece of this element of 450 kg, how much…

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

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Q: A breeder reactor converts relatively stable uranium-238 into the isotope plutonium-239. After 15…

A: Given:             dAdt=k 0.043% of total amount has disintegrated :              =100-0.043%…

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

A: Given that Radium-221 has a half life of 30 seconds. We need to calculate how long will it take for…

Q: determine how long it will take for 650 mg of a sample of chromium-51, which has a half life of…

A: Half Life-The half life of a substance is thetime taken for half of the substance tobreakdown or…

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

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Q: The decay equation for radon-222 gas is known to be y = y0 e-0.18t, with t in days. About how long…

A: The decay equation for radon-222 gas is known to be y = y0 e-0.18t, with t in days. About how long…

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

A: Let Q  = amount of substance present            dQdt=kQ             integrating on both sides…

Q: A radiation safety officer is working with 112 grams of a radioactive substance. After 17 days, the…

A: We have to find the decay rate of the radioactive compound.

Q: Element X is a radioactive isotope such that every 27 years, its mass decreases by half. Given that…

A: Radioactive decay

Q: Element X is a radioactive isotope such that every 28 years, its mass decreases by half. Given that…

A:

Q: 1. The radioactive isotope hydrogen-3 has a half-life of 12.3 years. a. If a sample of 80 mg of…

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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: 4. If caffeine has a half-life of 2 hrs., how many of 140 mg of caffeine remain in Mr. Moreno's…

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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.