The radioactive isotope of lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1 gram of this isotope is present initially, how long will it take for 90% of the 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: 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: 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: The radioactive isotope of lead Pb-209, decays at a rate proportional to the amount present at any…

A: The differential equation for decay is dAdt=kA dAA=k·dt ⇒∫dAA=∫k·dt⇒lnA=kt+c1A=ekt+c1A=ektec1A=Cekt…

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​ 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: 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: The radioactive isotope Carbon-14 has a half-life of 5,730 years. Given 300 grams of C-14, what is…

A: topic - exponential function

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

A: Definition used -                            Decay equation -…

Q: Radium decomposes at a rate proportional to the quantity present. If at the end of 20 years…

A: Solution

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 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: How long will it take 70 grams of cobalt-60 to decay to 7 grams? The half-life of cobalt-60 is 5.3…

A: Given data is : Initial 70 gram of cobalt -60 A0=70 gram  Let after t years cobalt-60 decay to 7…

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 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: The half-life of polonium is 139 days, but your sample will not be useful to you after 95% of the…

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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 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 half-life of Carbon-14 is 7 years. How much of an initial 131 g sample will remain after 45…

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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: 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 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: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

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Q: A radioactive substance decays at a continuous rate of 17% per day.  After 8 days, what amount of…

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Q: The half - life of Cobalt - 60 is 15 years. How much of an initial 105 g sample will remain after 33

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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: 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: 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: a car sells for $12,500 and one year later it is valued at $11,375. find the decay rate of the car

A: Explanation of the answer is as follows

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

A:

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…

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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…

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

Q: The half-life of plutonium-241 is approximately13 years.a. How much of a sample weighing 4 g will…

A: The half-life of plutonium-241 is 13 years. A(t)=A0e-k tA02=A0e-k×13…

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

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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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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.