Share
Explore BrainMass

Half-Life

A half-life is the time needed for a amount of radioactive material to fall to half the amount as measured in the beginning of the time period. It describes the property of radioactive decay or the quantity which exists after exponential decay.

The half-life describes the quantity which has undergone exponential decay. The opposite to half-life is doubling time. The exponential decay half-life process can be described by three equations as seen below:

N(t)= N_0 (〖1/2)〗^(t⁄t_(1⁄2) ) (1)
N(t)= N_0 e^((-t)⁄τ) (2)
N(t)= N_0 e^(-λt) (3)

Where
N0 is the initial quantity of the substance that will decay
N(t) is the quantity that still remains after time t
T1/2 is the half-life of the decaying quantity
Τ is the mean lifetime of the decaying quantity
Λ is the decay constant of the decaying quantity.

For processes with two or more exponential-decay processes simultaneously the equation is as followed

1/T_(1⁄2) = 1/t_1 + 1/t_2 +⋯

Radioactive Decay with Half-Life Concept

I need some help in determining the half-life: 1. A radioactive source has a half life of 74 days and an activity of 370 MBq. what was the activity 30 days ago? 2. A radioactive source has a half life of 60 days. what is the relative activity after one week? 3. An 11- Ci Ir- 192 source is recieved on August 20. Regulator

A range of radioactive decay calculations and solutions

1. A source has a half-life of 12 hours and an initial activity of 10mCi. After 4 days what is its activity? 2. Calculate the % of activity remaining in a source after 10 half lives. 3. a. A radionuclide decays 1% in one day. Calculate the half life. b. A radionuclide decays 70% in one day. Calculate the half life. 4. A

Source activity

An Ir-192 HDR unit has an activity of 8.6 Ci on May 2. The treatment time for a vaginal cylinder is 300 seconds. If the treatment time for a similar treatment is not to exceed 10 minutes, the source must be changed on: A. July 15 B. June 23 C. July 1 D. August 5

Half life formulas

Use the appropriate half life formula for the case described below. Discuss whether the formula is valid for the case described. Poaching is causing a population of zebras to decline by 8% per year. What is the half life of the population? If there are 10,000 zebras today, how many will remain in 60 years? Does

Radioactive element decays

A radioactive substance containing N(t) radioactive elements at time t decays according to the following rule: dN/dt = -kN with K > 0. Calculate the half-life T as function of k. T is definded as the time needed to decrease by a factor 2 the number of radioactive elements.

Half life problem

The half-life (the time required for the body to eliminate one-half of the total amount of caffeine) varies widely depending on factors such as: age; liver function; pregnancy; medications. In healthy adults, the half life is approximately 5 hours. Mr. Math LOVES McDonald's Diet Coke, and drinks the big 32oz one, which contains

Nuclear Decay for Radioactive Sources

Three radioactive sources each have activities of 1.0 micro Curies (Ci) at t=0. Their half lives are 1 sec, 1 hour and 1 day respectively a.) how many radioactive nuclei are present at each source when t=0 b.)how many nuclei of each source decay between t=0 and t=1sec c.)how many nuclei of each source decay between t=0

Analysis of administration of drugs using differential eqns

A drug that has an half life of 20 hours inside the human body and is administered intravenously (I.V.) into a patient. The rate of change of the drug in the body is proportional to the amount present. Write a differential equation explaining the rate of change of the quantity of the drug and determine the constant proportio

Half-Life of a Mixture

Would you help me with the following problem? An assay of an equilibrium ore mixture shows an atomic ratio for U-235 / Pa-231 of 3.04 X 10 ^6 . Calculate the half-life of U-235 from the assay data and the known half-life of Pa-231 (3.28 x 10^4 y). Ignore the Th(231) decay product.

Exploring the decay of Plutonium 241

Pu-241 is produced from neutron absorption by Pu-240 (which is produced by neutron absorption by Pu-239). Calculate the fractional in-growth of Am-241 from Pu-241 (i.e. number ratio Am-241/Pu-241) from time = 0 to 200 years. Pu-241 is the parent and Am-241 is the daughter.

Land of Lostistan Inflation Rate

In the land of Lostistan, the rate of inflation is 2%. This means that the value of money of Lostistan is continuously decreasing at a rate of 2% per year. (a) If a citizen of this country has a ten dollar bill in his pocket today, how much will those ten dollars be worth in ten years? (b) How much will ten dollars be worth

Calculating Mass and Decay: Example Questions

Part 1: (7-atomic mass)Be decays with a half-life of about (53-atmic mass) d. It is produced in the upper atmosphere, and filters down onto the Earth's surface. If a plant leaf is detected to have 374 decays/s of (7-atomic mass)Be, how many days do we have to wait for the decay rate to drop to 14.2/s? Part 2: Calculate

Decay rates: Which of the statements are true about decay rates and half-life?

Which of the following statements are true about decay rates and half-life? True False a large decay constant implies a long half-life True False in carbon dating, the radioactive isotope of carbon that is used is carbon-12 True False half-life is the time it takes for a radioactive sample to decay away to nothing

PP1 chain in stars like the Sun

Could you please explain the origin of each term in the uppermost equation in the file attached? (As the problem asks) Please explain also the origin of the number (2 and 1/2). H stands for Hydrogen and D for Deuterium. pp stands for proton-proton reaction and p-d for proton-deuterium reaction. The other 3 equations should help.

Migration of Pesticide from Soil to Groundwater

The following percentages of three pesticides added to a soil remained after increasing times. Time (days) Diazinon % Benefin % Terbutol % 0 100 100 100 15 18.7 no data no data 30 1.50 57.5 94.3 60 0.30 29.0 80.2 90 0.01 14.5 73.7 180 0.01 7.50 51.3 1) Fit the decomposition data f

Determining Amount of Radioactive Waste Created: Example Problem

A certain nuclear power plant produces radioactive waste in the form of strontium-90 at the constant rate of 500 pounds per year. The waste decays exponentially with a half life of 28 years. How much of the radioactive waste from the nuclear plant will be present after 140 years? (hint: Think of this as a survival and renewal pr

Radioactivity

Please help with the following problem. The number of unstable nuclei remaining after a time t=5.00 yr is N, and the number present initially is N 0. Find the ratio N/N0 for (a) ^14/6C (half-life=5730 yr), (b) ^15/8O (half-life=122.2x; use t=1.00h, since otherwise the answer is out of the range of your calculator), and (c) ^

Fossilized dinosaur skull and carbon-14 decay

A fossil dinosaur skull has been found in Montana and has been C-14 dated to be 73 million years old. Provide two scientifically based reasons to explain why C-14 dating cannot do this.

The half-life of tritium is approximately 12 years.

I have been stuck on this problem for ever! I am not good with ratios and I have no idea what equation I need to solve this problem. Please help, thank you. The half-life of tritium is approximately 12 years. What will be the molar ratio of tritium to helium-3 in a sealed sample after 25 years?

Lorentz transformation, length contraction, and time dilation.

My question is in three parts and asks for a relation between two space time intervals, an explanation of length contraction and time dilation, then an application of proper time. i) Two inertial frames O and O' are in standard configuration. Write down the two equations relating spacetime intervals Delta x' and Delta t' in

How to Calculate Half Life Problems

Provide a process for solving half-life problems. Example: An isotope of cesium (cesium-137 has a half -life of 30 years. If 1.0 mg of cesium-137 disintegrates over a period of 90 years, how many mg of cesium-137 would remain?

Half life of carbon-14

Carbon-14 datin of ancient objects requires that material to be organic in order to assay its age. You hear someone sat that a dinosaur bone ws carbon dated to be 75 million yaers old. What are two specific reasons that this claim is incorrect?

Quantization of Subatomic Particle

The muon is a subatomic particle with the same charge as an electron but with a mass that is 207 times greater. m_u = 207m_e. Physicists think of muons as "heavy electrons". However, the muon is not a stable particle; it decays with a half-life of 1.5 microseconds into an electron plus two neutrinos. Muons from cosmic rays are s