Radium decay constant

If ps (kg m-3) is the bulk soil density, AR (Bq kg-1) the specific activity of radium in the soil, a the emanating coefficient, and A (s-1) the decay constant of radon, then PsARa atoms, or psARaX Bq of radon, enter the interstitial air per m3 of soil volume per second. At depth in the soil, the rates of entry and radioactive decay of radon are equal, so its activity in interstitial air is... 

The decay constant of 220Rn is 6000 times greater than that of 222 Rn, so from (1.4) L is about 80 times less, that is only about 1 cm. The fraction of 220Rn atoms which escape from the rock crystals to the interstitial air is apparently about the same as for 222Rn, and since the specific activities of the thorium and radium chains are similar, equation (1.6) implies that the emanation of 222Rn should be 80 times greater... 

At the beginning of the twentieth century, research turned to the newly discovered radioactive substances. Ramsay and Soddy (1903) showed that helium was derived by radioactive disintegration of radium, the ftrst demonstration that one element was derived from another. Once the decay constant of radium had been determined, the door was open for the ftrst application of the noble gases geochronology (Strutt, 1908), a methodology that has been pursued ever since. 

Radium is element number 88, in which all of its isotopes are radioactive hence, what little radium is found on Earth is mostly as a trace element in uranium ores. The most common isotope has a mass number of 226 with a half-life of 1,604 years. The second longest-lived isotope is radium 228, with a half-life of 5.77 years. The other isotopes have much shorter half-lives ranging from microseconds to days. Radium is constantly being formed as part of the radioactive decay series of uranium and thorium. Because it decays so quickly, however, only minute quantities of radium ever exist at any one time. 

In this equation D (m2.s 1) represents the radon diffusivity, X the radioactive decay constant (s 1), C (Bq.m3) the radon concentration in the pore space, R (Bq.kg1) the radium concentration in the material, p (kg.m3) the bulk density of the dry material, E (dimensionless) the radon emanation power coefficient for the pore spaces, s (dimensionless) the total porosity and 0 (dimensionless) the moisture. The solution of the diffusion equation for an homogeneous medium represents the flux release from the waste material to the surface, Jt (Bq.m 2.s ). For a system without cover we obtain (Rogers, 1984) ... 

This result is used in problem 14 for estimating Avogadro s number and in problem 168 for determining the decay constant of radium. 

To determine the decay constant of radium from the rate of emission of a-particles. 

Taking the atomic weight of radium as 226 g mole and Avogadro s number as 0.602 x 10 mole" we obtain for the decay constant... 

To estimate the decay constant of uranium from the radium content of a uranium mineral. 

Example 10-1, The half-life of radium (ggRa-- ) is 1590 years. What is the value of the decay constant What fraction decays in one year ... 

You can obtain the decay constant for a radioactive nucleus by counting the nuclear disintegrations over a period of time. The original definition of the curie (now 3.7 X 10 disintegrations per second) was the activity or decay rate of 1.0 g of radium-226. You can use this with the rate equation to obtain the decay constant of radium-226. Radium-226 has a molar mass of 226 g. A 1.0-g sample of radium-226 contains the following number of nuclei ... 

The activity of a radioactive sample is the number of nuclear disintegrations per second, which is equal to the first-order rate constant times the number of radioactive nuclei present. The fundamental unit of radioactmty is the curie (Ci), where 1 Ci coiTesponds to exactly 3.70 X 10 ° disintegrations per second. This decay rate is equivalent to that of 1 g of radium-226. Calculate the rate constant and half-life for the radium decay. Starting with 1.0 g of the radium sample, what is the activity after 500 yr The molar mass of Ra-226 is 226.03 g/mol. 

This decay rate is equivalent to that of 1 g of radium-226. Calculate the rate constant and half-life for the radium decay. Starting with 1.0 g of the radium sample, what is the activity after 500 yr The molar mass of Ra-226 is 226.03 g/mol. 

The graph and Fig. 25-6 are almost exactly the inverse of one another, with the maxima of one being the minima of the other. 73a. The rate of decay depends on both the half-life and the number of radioactive atoms present. In the early stages of the decay chain, the larger number of radium-226, atoms multiplied by the very small decay constant is still larger than the product of the very small number of radon-2 atoms and its much larger decay constant. Only after some time has elapsed, does the rate of decay of radon-222 approach the rate at which it is formed from radium-226 and the amount of radon-222 reaches a maximum. Beyond this point, the rate of decay of radon-222 exceeds its rate of formation. 

The first-order rate constant for the radioactive decay of radium-223 is 0.0606 day L What is the half-life of radium-223 ... 

Very soon after the radioactivity of thorium and uranium had been discovered it was found that pure samples of both of these elements were only very weakly radioactive. However, such pure samples became more and more radioactive with time until they reached a steady level identical to that in the original samples before pmification. This suggested that the uranium or thorium atoms were transforming or decaying into other radioactive daughter elements and that hitherto undiscovered series of such elements might exist. The search for the radioactive products of uranium by Marie and Pierre Curie led to the characterisation of two new elements, which were named polonium, Po, and radium, Ra. Both elements are far more radioactive than uranium and decay so rapidly that no ore deposits are formed. They exist only because they are formed constantly from naturally occurring uranium. 

Radium-224 is radioactive and decays by emitting an a-particle. (a) Write an equation for this process, (b) The decay of radium-224 produces helium gas. Rutherford and Geiger determined that a-particles were emitted from ggRa at a rate of 7.65 x lO s moU, and that this corresponded to a rate of helium production of 2.90 X dm s at 273 K, 1 bar. If 1 mole of helium occupies 22.7 dm (273 K, 1 bar), estimate a value for the Avogadro constant. 

So, we see as a laboratory source of alpha particles the supply would be pretty constant over a long period of time. Another consideration is that radium is in the same column of the periodic chart as Ca and so biologically it might have similar chemistry to Ca and become trapped in bone tissue where it would be radioactive for a long time. Thus, this interlude regarding the fact that first-order decay is a useful model for nuclear processes has provided an opportunity to discuss some aspects of nuclear chemistry. Considering the crossover of physics and chemistry in the work of the Curies (Marie, Pierre, and Irene) and information in the popular domain regarding nuclear chemistry, we think this brief discussion is justified as an essential part of physical chemistry. 

Even though some of the daughters in natural radioactive decay schemes have very short half-lives, all are present because they are constantly forming as well as decaying. It is likely that only about one gram of radium-226 was present in several tons of uraniiun ore processed by Marie Curie in her discovery of radium in 1898. Nevertheless, she was successful in isolating it. The ore also contained only a fraction of a milligram of polonium, which she was able to detect but not isolate. 

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