Constant decay

Even if the homogeneous line shape can be extracted, many other processes can contribute. Every decay process contributes to the finite lifetime of an excited species. A, with an individual decay constant k ... 

Table B2.5.5. The photochemical decomposition of methyl radicals (UV excitation at 216 nm). ris tire wavenumber linewidth of the methyl radical absorption and /ris the effective first-order decay constant [54].

Fig. 10.19 The probability density of the extreme value distribution typical of the MSP scores for random sequena The probability that a random variable with this distribution has a score of at least x is given by 1 - exp[-e -where u is the characteristic value and A is the decay constant. The figure shows the probability density function (which corresponds to the function s first derivative) for u = 0 and A = 1.

From the radioactive decay constants and measurement of the amount of argon in a rock sample, the length of time since formation of the rock can be estimated. Essentially, the dating method requires fusion of a rock sample under high vacuum to release the argon gas that has collected through radioactive decay of potassium. The amount of argon is determined mass spectrometrically,... 

The decay constant is the key to the mixing rate number defined for Re > lO" by N/ D/TY = 0.5 for a disk flat blade turbine (DFBT), and N/ (D/TY = 0.9 for the propeUer. Therefore, power required to achieve any degree of uniformity in a fixed time is proportional to D and D for DFBT and propeUer, respectively. 

Radioactive waste is characterized by volume and activity, defined as the number of disintegrations per second, known as becquerels. Each radionucHde has a unique half-life,, and corresponding decay constant, A = 0.693/tj 2 For a component radionucHde consisting of JS1 atoms, the activity, M, is defined as... 

Half-Lives and Decay Constants. Each nuclear state, whether an unstable ground state or an excited level, has a characteristic probabiUty... 

Experimental measurements have shown that the following description of the decay is correct. If at any time, /, there are a large number of nuclei, N(t), in the same state which has the decay constant, A, then the change in the number of nuclei in this state in a short time, d/, is... 

In a description of nuclear properties, the half-life,, is quoted rather than the decay constant. This quantity is the time it takes for one-half of the original nuclei to decay. That is,... 

In almost all cases X is unaffected by any changes in the physical and chemical conditions of the radionucHde. However, there are special conditions that can influence X. An example is the decay of Be that occurs by the capture of an atomic electron by the nucleus. Chemical compounds are formed by interactions between the outer electrons of the atoms in the compound, and different compounds have different electron wave functions for these outer electrons. Because Be has only four electrons, the wave functions of the electrons involved in the electron-capture process are influenced by the chemical bonding. The change in the Be decay constant for different compounds has been measured, and the maximum observed change is about 0.2%. 

In spite of these special cases, in all appHed uses the decay constants and half-Hves can be considered to be independent of the physical and chemical environment. 

The above decay equations apply to the simple case of a radionucHde that is decaying without being replenished. There are many cases in which a nucHde is both being produced and decaying at the same time. One example is the case where one radioactive nucHde is produced by the decay of another nucHde (see Tables 1 and 2). If there are (0) atoms of nucHde 1, the parent, having decay constant A, decays to nucHde 2, the daughter, having decay constant X, then at t = 0 there are (0) such atoms present. Then... 

The decay constant, 1, dehnes the probability that a particular atom will decay within a given time (X = In The half-life describes a time interval after... 

FIG. 2 Charge density q z) (solid line) with its integral Q z) = q z )dz (dashed line) in presence of an adsorption potential and, in the case of asymmetrical ions, 0. The decay constants are /ci = 1 + 2/ and 2 = 1 — 2/. (Reprinted from Ref. 19 with permission from Elsevier Science.)... 

Copper-64 is one of the metals used to study brain activity. Its decay constant is 0.0546 h-1. If a solution containing 5.00 mg of Cu-64 is used, how many milligrams of Cu-64 remain after eight hours ... 

Fluorine-18 has a decay constant of 6.31 X 10-3 min-1. How many counts will one get on a Geiger counter in one minute from 1.00 mg of fluorine-18 Assume the sensitivity of the counter is such that it intercepts 0.50% of the emitted radiation. 

WEB Chlorine-36 decays by beta emission. It has a decay constant of 2.3 X 10-6 y-1. How many /3-particles are emitted in one minute from a 1.00-mg sample of Cl-36 How many curies does this represent ... 

Smoke detectors contain small amounts of americium-241. Am-241 decays by emitting a-particles and has a decay constant of 1.51 X 10-3 y 1. If a smoke detector gives off ten disintegrations per second, how many grams of Am-241 are present in the detector ... 

The principle behind the home smoke detector is described on page 516. Americium-241 is present in such detectors. It has a decay constant of 1.51 X 10-3 y 1. You are urged to check the battery in the detector at least once a year. You are, however, never encouraged to check how much Am-241 remains undecayed. Explain why. 

In this context, k is called the decay constant. The law tells us that the activity of a radioactive sample is proportional to the number of atoms in the sample. As we saw in Section 13.4, a first-order rate law implies an exponential decay. It follows that the number N of nuclei remaining after a time t is given by... 

One of the reasons why thermonuclear weapons have to be serviced regularly is the nuclear decay of the tritium that they contain. Suppose a tritium sample of mass 1.00 g is stored. What mass of that isotope will remain after 5.0 a (1 a = 1 year) The decay constant of tritium is 0.0564 a-1. 

Self-Test 17.5A The decay constant for fermium-254 is 210 s. What mass of the isotope will be present if a sample of mass 1.00 xg is kept for 10. ms ... 

Self-Test 17.5B The decay constant for the nuclide neptunium-237 is 3.3 X... 

Predict the amount of a radioactive sample that will remain after a given time period, given the decay constant or half-life of the sample (Example 17.3). 

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