A certain specimen of charcoal contains 55% of Carbon – 14 as compared to a charcoal at present day. If the decay factork = 0.0001216 per year. Determine the age of the charcoal and the half – life of the specimen.

Q: Radiocarbon C14 has a half-life of 5730 years. How many years will it take for 26%of a sample of C14…

A:

Q: The isotope cesium-137 has a half-life of 29.75 years. How long will it take a 100 gram sample of…

A: To determine the time taken for 100 gram sample of cesium-137 to decay to 75 grams.

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

A:

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

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, then the decay constant λ by…

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: 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: A fragment of bone is discovered to contain 20% of the usual 14C concentration. Estimate the age of…

A:

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

A:

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

A:

Q: If a piece of charcoal made from wood of a tree shows only 62% of the carbon 14 expected living in…

A:

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

A:

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

A:

Q: A sample of tritium-3 decayed to 85% of its original amount after 4 years. How long would it take…

A: Given problem:- A sample of tritium-3 decayed to 85% of its original amount after 4 years. How long…

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: 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: 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: The half-life of carbon-14 is known to be 5720 years. Doctor Frankenstein has 300 grams of…

A: From the given data:

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: There are 5,000 wolves in the park, but their population is expected to decay at a rate of 8% per…

A: Given, initially , wolves in the park = 5000 Decay of population = 8% per year finally , wolves in…

Q: If the starting point is 900, and the decay rate is 3%, choose the exponential function.

A: Starting point refers to the initial value. Decay rate is 3% = 0.03

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: 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: 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: 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: 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: A radioactive substance has a decay rate of 4% per hour. If 1000 grams of the substance are present…

A: It is given that,a radioactive substance has a decay rate of 4% per hour. If 1000 grams of the…

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

A:

Q: The half-life radium-226 is 1622 years. Find its decay constant.

A:

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

A:

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

A:

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…

A:

Q: alf-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only…

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: 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: After 25 years, 60% of a radioactive substance still remains in a 20 gram sample. What is the…

A: Half life of a radio active material is the time required to reduce the initial quantity to its…

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

A:

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

A:

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.