Half lifes

The half-life measures the time it takes for the radiation coming off any mass of an isotope to drop to half its value. Short half-lives of hours or minutes mean that these isotopes give off radiation at such a rate that they deliver their radiation in a short time. Often, the shorter the half-life, the more energetic and more harmful the radiation. 

To ensure that people working with radioactive materials are protected from the harmful effects of radiation, they wear photographic badges. These are developed periodically and the greater the exposure to radiation, the greater the fogging . When the value becomes too high, the worker is taken off the work task. 

Radiation is also detected using Geiger counters, which convert the incoming radiation to a click. The greater the intensity of the clicks, the greater amount of radioactive material present. These instruments always click in ordinary air because there is always some radiation entering a room from space, from the stone of the building or the rocks below. 

There are limits to what is permitted for each user and this is governed by the Health and Safety regulations. The same applies to people working with X-rays. A good set of free wall charts is available from the National Radiological Protection Board (NRPB)1 that summarizes all these processes. 

Isotopes of varying half-lives are used extensively in medicine both for diagnosis and also treatments (Table 12.1). A typical example of medical use of an isotope is 

The half-life (T) of a reaction is an important term that may be derived from equation (9.1). The half-life is defined as the time taken for the concentration of reactant to fall to half its original value  

For first-order reactions (only), U is independent of concentration. This means that the time taken for the reactant concentration to fall from 1 m to 0.5 M will be the same as the time taken to fall from 0.5 M to 0.25 M. This is not true for higher orders of reaction and occasionally this fact is used to infer that a reaction is first order. 

The half-life indieates how long it takes before the activity is decreased to half of the initial level. It is denoted by ty, and given by  

The half-life for radioactive nuclei varies significantly from one species to another. E.g. has the Uranium- 

Is the half-life known it is possible to calculate a value for the decay constant k which thereby may be used in calculations of the activity and the number of radioactive nuclei to a given time. 

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The half-life of a reaction, t 2 is the time required for the concentration of a reactant to reach half its initial value, fA]tj, = [A]q. Half-life is a convenient way to describe how fast a reaction occurs, especially if it is a first-order process. A fast reaction has a short half-life. 

From Equation 14.15, we see that fi/2 for a first-order rate law does not depend on the initial concentration of any reactant. Consequently, the half-life remains constant throughout the reaction. If, for example, the concentration of a reactant is 0.120 M at some instant in the reaction, it will be y(0.120 M) = 0.060 M after one half-life. After one more half-life passes, the concentration wiU drop to 0.030 M, and so on. Equation 14.15 also indicates that, for a first-order reaction, we can calculate tj/2 if we know k and calculate k if we know ti/i- 

If a solution containing 10.0 g of a substance reacts by first-order kinetics, how many grams remain after 3 half-lives  

A FIGURE 14.11 Knelicdatafortherearrangmentof methyl isonilrile to acetonitrfie at 199 °C, showing the half-Bfe of the reaction. 

Methyl bromide is removed from the lower atmosphere by a variety of mechanisms, including a slow reaction with ocean water  

We can determine the half-life of a first-order reaction by substituting [ f [ A]o 

The half-life of a reactant is the time it takes for its concentration to fall to one-half its original value. Although this quantity can be defined for any reaction, it is particularly meaningful for first-order reactions. To see why, let s remrn to the system we considered in Example Problem 11.5, the photodissociation of ozone by UV light in the upper atmosphere. 

25 atm, or one-fourth of its initial value after about 38 hours. In the first 19-hour period, the ozone pressure decreased by one-half its value from 1 to 0.5. Between about 19 hours and 38 hours on the graph, the pressure again decreased by one-half, this time falling from 0.5 to 0.25. For the particular conditions of this experiment, the ozone pressure decreases by a factor of 2 for every 19 hours. So the half-life is constant, no matter how much ozone we start with. 

We can obtain a mathematical expression for the half-life of a first-order reaction by substituting in the integrated rate law (Equation 11.5). By definition, when the reaction has been proceeding for one half-life (ti/2), the concentration of the reactant must be [X] = j[X]q. Thus we have 

Solving this equation for the half-life gives 

Equation 11.8 relates the half-life of any first-order reaction to its rate constant. Because k does not depend on the amount of substance present, neither does t. The half-life is most often used to describe the kinetics of nuclear decay. All 

The radioactive half-life for a given radioisotope is the time it takes for half of the radioactive nuclei in any sample to undergo radioactive decay. After two half-lives, one-fourth of the original sample will be left, after three half-lives one-eighth of the original sample will be left, and so forth. 

The rate of radioactive decay is typically expressed in terms of either the radioactive half-life or the radioactive decay constant. They are related as follows  

The decay constant is sometimes also called the disintegration constant. The half-life and the decay constant give the same information, so either may be used to characterize decay. Another useful concept in radioactive decay is the average lifetime. Average lifetime is the reciprocal of decay constant. 

As previously discussed, the half-life of a reaction is defined as the time it takes for the concentration of the reactant to fall to half of its initial value. Determining the half-life of a reaction as a function of the initial concentration makes it possible to calculate the reaction order and its specific reaction rate. 

Consider the reaction A — products. The rate equation in a constant volume batch reaction system gives 

Rearranging and integrating Equation 3-82 with the boundary conditions t = 0, CA = CAO and t = t, CA = CA gives 

In all cases x is the amount of reactant A consumed per unit volume, and except in the autocatalytic case x = 0 when / = 0  

Source Laidler, K. J., Chemical Kinetics, 3rd ed. Harper Collins Publishers, 1987. 

Consider the reaetion A — produets. The rate equation in a eonstant volume bateh reaetion system gives 

Common unit for Relationship between rate constant rate constants 

In all discs a is tlie nmoiint of renctant A consimictl per unit volume, iiml exci i ) in the aiilocalal lic case, v — 0 wlien i - 0 

From a conceptual approach, we can look at half-life as the time it takes for of a sample to decay into some other substance. For instance, if we start out with 1.0 g of a radioactive sample, after one half-life has elapsed, we will be left with only 0.5 g of the original material. After two half-lives, we will have 0.25 g. After 3, 0.125 g. As you can see, this could go on for some time, but it is generally accepted that after about 10 half-lives have elapsed, there is a negligible amount of the original radioactive material left. 

Most of the problems on past AP tests that contain half-lives are relatively simple to solve, using either conceptual or mathematical approaches. On the test, you are not provided with any equations related to nuclear chemistry. Therefore, any calculations you will have to make should be fairly simplistic and easy to solve using a few simple rules. From a conceptual 

If you start with 64 g of a material with a half-life of 10 years, how much will be left at the end of 40 years  

Conceptually, you can work through this step-by-step  

The conceptual approach is particularly effective when solving problems that have half-lives that are whole number values. For more complex problems, we need to use some ideas 

A common parameter used in the characterization of enzyme stability is the half-fife (0/2). As described in Chapter 1, the reaction half-life for a first-order reaction can be calculated from the rate constant  

The half-life has units of time and corresponds to the time required for the loss of half of the original enzyme concentration, or activity. 

All radioactive elements do not decay at the same pace. They have drastically different rates of decay. The radioactive decay time is expressed in terms of half-life period. The half-life of a radioactive substance is the time required for the decay of half the substance present in a sample of that substance. 

Regardless of the amount of a particular radioactive substance we have, it takes the same time (half-life) to complete the decay of half the number of nuclei in that sample. 

The half-life of a radioactive substance is the time required for the complete decay of exactly half the amount of that substance. 

Calculate the amount of time (in years) it takes for the decay of 75% of a given sample of carbon-14. Carbon-14 has a half-life of approximately 5700 years. 

After the first 5700 years of decay, 50% of the original sample is left. After 5700 more years, 50% of that sample will have decayed, which means that there is now 25 % of the original intact sample. This is the amount of time that the question is asking for. To be clear about our analysis, let s rephrase what we have said. We have 25% of the original sample left at this point. Thus the decay of 75% of the original sample is complete. So the answer is 5700 x 2 = 11400 years. 

Each radioactive nuclide decays at its own characteristic rate. That rate is completely independent of the temperature, pressure, or volume of the sample, or whether the sample is a pure element, part of a compound, or part of a mixture. The most convenient way to distinguish the decay rate of different nuclides is to state their half-lives. The half-life (ti ) of a radioactive substance is the time it takes for one half of the atoms that were present 

If one half of the atoms initially present decay during the first half-life, then one half of the initial atoms are still left. Then, one half of those atoms will decay during the second half-life, so that one-quarter of the initial atoms are still left. One half of those will decay during the third half-life, leaving one-eighth of the initial atoms remaining, and so forth. 

The calculation of clearance using this equation is illustrated by the following example. Aspirin is metabolized primarily in the liver. Normal hepatic blood flow (Q) equals 1500 mL/min. If the blood entering the liver contains 200 fxg/mL of aspirin (Ci) and the blood leaving the liver contains 134 fxg/mL (Co), hepatic clearance of aspirin is calculated as follows  

This example illustrates that clearance is actually the amount of plasma that the drug can be totally removed from per unit time. As calculated here, the liver would be able to completely remove aspirin from 495 mL of blood each minute. Tetracycline, a common antibacterial drug, has a clearance equal to 130 mL/min, indicating that this drug would be completely removed from approximately 130 mL of plasma each minute. 

Clearance is dependent on the organ or tissue s ability to extract the drug from the plasma as well as the perfusion of the organ. Some tissues may have an excellent ability to remove the drug from the bloodstream, but clearance is limited because only a small 

In terms of drug elimination from the entire body, systemic clearance is calculated as the sum of all individual clearances from all organs and tissues (i.e., systemic CL = hepatic CL + renal CL + lung CL, and so on). Note that the elimination of the drug includes the combined processes of drug loss from the body (excretion) as well as inactivation of the drug through biotransformation.7 58 60 

Half-life is a function of both clearance and volume of distribution (Vd) 38 that is, the time it takes to eliminate 50 percent of the drug depends not only on the ability of the organ(s) to remove the drug from the plasma, but also on the distribution or presence 

Not all the nuclei of a given sample of a radioactive isotope disintegrate at the same time, but do so over a period of time. The number of radioactive disintegrations per unit time that occur in a given sample of a naturally radioactive isotope is directly proportional to the quantity of that isotope present. The more nuclei present, the more will disintegrate per second (or per year, etc.). 

EXAMPLE 19.3. Sample A of has amass of 0.500 kg sample B of the same isotope has amass of 1.00 kg. Compare the rate of decay (the number of disintegrations per second) in the two samples. 

There will be twice the number of disintegrations per second in sample B (the 1.00-kg sample) as in sample A, because there were twice as many atoms there to start. The number of disintegrations per gram per second is a constant, because both samples are the same isotope— 

500 kg takes 1 half-life to undergo the process shown for sample A, it also should take the same 1 half-life to undergo the process shown for sample B, after sample B gets down to 0.500 kg. 

EXAMPLE 19.4. A certain isotope has a half-hfe of 3.00 years. How much of a 8.00-g sample of this isotope will remain after 12.0 years  

These are just general guidelines, and they do not work for all elements. 

Most of the problems on past AP exams that contain half-lives are relatively simple to solve, using either conceptual or mathematical approaches. On the exam, you are not provided with any equations related to nuclear chemistry. Therefore, any calculations you will have to make should be fairly simplistic and easy to solve using a few simple rules. From a conceptual perspective, this that means half-life problems can be solved by repeatedly cutting the starting amount in half. For example, after one half-life, a sample will have 14 the number of radioactive nuclei that it started with. After two half-lives, the sample will have (y)(y),or(y), times the number of radioactive nuclei left. After three half-lives, the sample will have () )( )() ), or (), times the number of radioactive nuclei left. If you haven t already spotted the pattern here, it is that the amount of sample left after time t will be 

If you chose to live in a radiation-proof home to escape radiation originating from outer space, you would still have to contend with the radiation that is naturally in your body. If you weigh 150 pounds, you have about 225 grams of potassium ions in your body. Potassium ions participate in nerve conduction and the contraction of muscles, including the heart. Without potassium ions, you don t live. The natural abundance of is 0.0118% of all potassium ions. A 150-pound person therefore has about 4.1 X 10 ° radioactive i°K atoms in his or her body. (You might like to confirm this statement by calculation. We ll show the calculation setup after the Target Check answers.) 

What is the easiest way you can protect yourself from the harmfiil effects of natural sources of radiation  

The rate at which a radioactive substance decays is measured by its half-life, the time it takes for one half of the radioactive atoms in a sample to decay. Each radionuclide has its own unique half-life, commonly written ty2. The units of units per 

The half-life of gsBi is 5.0 days. If you begin with 16 grams of ssBi, how many grams will you have left 25 days (5 half-lives) later  

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The C exchanges with C in living organisms, but exchange ceases on death. The radioactive content decays with a half-life of 5730 years. Hence the age of a once living material may be established by determining the amount of C. 

For trace quantities of less than 100 ppm, the most successful method — and the most costly— is neutron activation. The sample is subjected to neutron bombardment in an accelerator where oxygen 16 is converted to unstable nitrogen 16 having a half-life of seven seconds. This is accompanied by emission of (J and 7 rays which are detected and measured. Oxygen concentrations as low as 10 ppm can be detected. At such levels, the problem is to find an acceptable blank sample. 

The choice of tracer gas for the measurements is Kr-85 It has a long half-life so that it can be stored for application when needed. It is a noble gas which is chemically inactive giving a low radio toxicity as it is readily removed in case of accidental contamination. 

Table C2.6.5 Rapid coagulation half-life time for particles in water at 7 =300 K (equation (C2.6.16)).

Figure 10.3-13. s-Triazine herbicides and their half-life ill soil [16],... 

An ideal" drug must be safe and effective. The mavimum daily dose should not exceed 200-300 mg. Drugs should be well absorbed orally and bioavailablc. Metabolic stability ensures a reasonable long half-life. Further on, a drug should be non-... 

Carbon has seven isotopes. In 1961 the International Union of Pure and Applied Chemistry adopted the isotope carbon-12 as the basis for atomic weights. Carbon-14, an isotope with a half-life of 5715 years, has been widely used to date such materials as wood, archaeological specimens, etc. 

Seventeen isotopes of potassium are known. Ordinary potassium is composed of three isotopes, one of which is 40oK (0.0118%), a radioactive isotope with a half-life of 1.28 x IO9 years. 

Natural vanadium is a mixture of two isotopes, 50V (0.24%) and 51V (99.76%). 50V is slightly radioactive, having a half-life of > 3.9 x 10i7 years. Nine other unstable isotopes are recognized. 

Thirty isotopes are recognized. Only one stable isotope, 1271 is found in nature. The artificial radioisotope 1311, with a half-life of 8 days, has been used in treating the thyroid gland. The most common compounds are the iodides of sodium and potassium (KI) and the iodates (KIOs). Lack of iodine is the cause of goiter. 

Polonium-210 is a low-melting, fairly volatile metal, 50% of which is vaporized in air in 45 hours at 55C. It is an alpha emitter with a half-life of 138.39 days. A milligram emits as many alpha particles as 5 g of radium. 

Twenty five isotopes of polonium are known, with atomic masses ranging from 194 to 218. Polonium-210 is the most readily available. Isotopes of mass 209 (half-life 103 years) and mass 208 (half-life 2.9 years) can be prepared by alpha, proton, or deuteron bombardment of lead or bismuth in a cyclotron, but these are expensive to produce. 

Twenty isotopes are known. Radon-22, from radium, has a half-life of 3.823 days and is an alpha emitter Radon-220, emanating naturally from thorium and called thoron, has a half-life of 55.6 s and is also an alpha emitter. Radon-219 emanates from actinium and is called actinon. It has a half-life of 3.96 s and is also an alpha emitter. It is estimated that every square mile of soil to a depth of 6 inches contains about 1 g of radium, which releases radon in tiny amounts into the atmosphere. Radon is present in some spring waters, such as those at Hot Springs, Arkansas. 

Gr. aktis, aktinos, beam or ray). Discovered by Andre Debierne in 1899 and independently by F. Giesel in 1902. Occurs naturally in association with uranium minerals. Actinium-227, a decay product of uranium-235, is a beta emitter with a 21.6-year half-life. Its principal decay products are thorium-227 (18.5-day half-life), radium-223 (11.4-day half-life), and a number of short-lived products including radon, bismuth, polonium, and lead isotopes. In equilibrium with its decay products, it is a powerful source of alpha rays. Actinium metal has been prepared by the reduction of actinium fluoride with lithium vapor at about 1100 to 1300-degrees G. The chemical behavior of actinium is similar to that of the rare earths, particularly lanthanum. Purified actinium comes into equilibrium with its decay products at the end of 185 days, and then decays according to its 21.6-year half-life. It is about 150 times as active as radium, making it of value in the production of neutrons. 

In 1964, workers at the Joint Nuclear Research Institute at Dubna (U.S.S.R.) bombarded plutonium with accelerated 113 to 115 MeV neon ions. By measuring fission tracks in a special glass with a microscope, they detected an isotope that decays by spontaneous fission. They suggested that this isotope, which had a half-life of 0.3 +/- 0.1 s might be 260-104, produced by the following reaction 242Pu + 22Ne —> 104 +4n. 

New data, reportedly issued by Soviet scientists, have reduced the half-life of the isotope they worked with from 0.3 to 0.15 s. The Dubna scientists suggest the name kurchatauium and symbol Ku for element 104, in honor of Igor Vasilevich Kurchatov (1903-1960), former Head of Soviet Nuclear Research. 

The discoveries at Berkeley were made by bombarding a target of 249Cf with 12C nuclei of 71 MeV, and 13C nuclei of 69 MeV. The combination of 12C with 249Cf followed by instant emission of four neutrons produced Element 257-104. This isotope has a half-life of 4 to 5 s. 

The same reaction, except with the emission of three neutrons, was thought to have produced 258-104 with a half-life of about 1/100 s. 

Element 259-104 is formed by the merging of a 13C nuclei with 249Cf, followed by emission of three neutrons. This isotope has a half-life of 3 to 4 s, and decays by emitting an alpha particle into 255No, which has a half-life of 185 s. 

Element 106 was created by the reaction 249Gf(180,4N)263X, which decayed by alpha emission to rutherfordium, and then by alpha emission to nobelium, which in turn further decayed by alpha between daughter and granddaughter. The element so identified had alpha energies of 9.06 and 9.25 MeV with a half-life of 0.9 +/- 0.2 s. 

At Dubna, 280-MeV ions of 54Gr from the 310-cm cyclotron were used to strike targets of 206Pb, 207Pb, and 208Pb, in separate runs. Foils exposed to a rotating target disc were used to detect spontaneous fission activities. The foils were etched and examined microscopically to detect the number of fission tracks and the half-life of the fission activity. 

In 1957 workers in the United States, Britain, and Sweden announced the discovery of an isotope of element 102 with a 10-minute half-life at 8.5 MeV, as a result of bombarding 244Gm with 13G nuclei. On the basis of this experiment, the name nobelium was assigned and accepted by the Gommission on Atomic Weights of the International Union of Pure and Applied Ghemistry. 

The acceptance of the name was premature because both Russian and American efforts now completely rule out the possibility of any isotope of Element 102 having a half-life of 10 min in the vicinity of 8.5 MeV. Early work in 1957 on the search for this element, in Russia at the Kurchatov Institute, was marred by the assignment of 8.9 +/- 0.4 MeV alpha radiation with a half-life of 2 to 40 sec, which was too indefinite to support discovery claims. 

Gonfirmatory experiments at Berkeley in 1966 have shown the existence of 254-102 with a 55-s half-life, 252-102 with a 2.3-s half-life, and 257-102 with a 23-s half-life. 

Ten isotopes are now recognized, one of which — 255-102 — has a half-life of 3 minutes. 

Searches for the element on earth have been fruitless, and it now appears that promethium is completely missing from the earth s crust. Promethium, however, has been identified in the spectrum of the star HR465 in Andromeda. This element is being formed recently near the star s surface, for no known isotope of promethium has a half-life longer than 17.7 years. Seventeen isotopes of promethium, with atomic masses from 134 to 155 are now known. Promethium-147, with a half-life of 2.6 years, is the most generally useful. Promethium-145 is the longest lived, and has a specific activity of 940 Ci/g. 

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