That equations between half-life period and life are tried to look for is the main aim in this paper. Several curves are found here. It hopes that these curves are useful to wield its roles in current research. D wave molecule in quantum dynamics is found to have a short (~several hundred ms) life. So that it is calculated that the N/N0 and radioactivity at a certain life. Through comparing we find the radioactivity is more important than the N/N0, the radioactivity is first factor and then N/N0. It is found that N/N0 decreases with decay constant increasing and the radioactivity increases and then decreases with it increasing. It increases and then decreases if N/N0 increases. The maximum value of 1.7 nuclei of radioactivity is not so big explains no neglect is available. It is old after 0.22 years. D wave molecule in quantum dynamics is found to have a short (~several hundred ms) life. So that it is calculated that the N/N0 and decay constant with half-life period at a certain time. Through comparing we find the half-life period is more important than the decay constant, it is first factor and then decay constant. It is found that N/N0 increases with half-life period increasing and it decreases with life decreasing too. The frequency and energy decrease if D wave increases. If we activate two areas two D wave molecules will be activated. In terms of that calculating half period life will double, promoting areas for four will increase life four times. Continuous utilizing this the 0.22years half one will attain 22years. The needed one is the material whose volume is big enough to produce one. Like Copper oxidation etc. Heard can be applied to the quantum CPU. How we can calculate this material whose D wave molecule life is bigger than now is the key.
That equations between half-life period and life are tried to look for is the main aim in this paper. Several curves are found here. It hopes that these curves are useful to wield its roles in current research. D wave molecule in quantum dynamics is found to have a short (~several hundred ms) life. So that it is calculated that the N/N0 and radioactivity at a certain life. Through comparing we find the radioactivity is more important than the N/N0, the radioactivity is first factor and then N/N0. It is found that N/N0 decreases with decay constant increasing and the radioactivity increases and then decreases with it increasing. It increases and then decreases if N/N0 increases. The maximum value of 1.7 nuclei of radioactivity is not so big explains no neglect is available. It is old after 0.22 years. D wave molecule in quantum dynamics is found to have a short (~several hundred ms) life. So that it is calculated that the N/N0 and decay constant with half-life period at a certain time. Through comparing we find the half-life period is more important than the decay constant, it is first factor and then decay constant. It is found that N/N0 increases with half-life period increasing and it decreases with life decreasing too. The frequency and energy decrease if D wave increases. If we activate two areas two D wave molecules will be activated. In terms of that calculating half period life will double, promoting areas for four will increase life four times. Continuous utilizing this the 0.22years half one will attain 22years. The needed one is the material whose volume is big enough to produce one. Like Copper oxidation etc. Heard can be applied to the quantum CPU. How we can calculate this material whose D wave molecule life is bigger than now is the key.
D wave molecule in quantum dynamics is found to have a short (~several hundred ms) life. So that it is calculated that the N/N0 and time at a certain life which is 0.2s, 0.32s and 0.49s. Through comparing we find the life is more important than the time, it is first factor and then passing time. The frequency and energy decrease if D wave increases. D wave molecule in quantum dynamics is found to have a short (~several hundred ms) life. So that it is calculated that the N/N0 and decay constant with half-life period at a certain time. Through comparing we find the half-life period is more important than the decay constant, it is first factor and then decay constant. It is found that N/N0 increases with half-life period increasing and it decreases with life decreasing too.
Instead of counting the number of nuclei ( ),tN it is easier to count the rate at which decays occur in the radioactive sample, and this is called the activity, defined as ( )0 tdN N e Ndt λλ λ−= = t (47.5) and follows the same exponential decay law (47.3). The SI unit for activity is the Becquerel (Bq), equal to one decay per second, and the common unit is the Curie (Ci), defined as It is also convenient to introduce the half-life as the time interval in which the activity is reduced to one-half .Bq107.3Ci1 10×= 2/1t 2ln2ln2/1 τλ ==t (47.6) The probability of radioactive decay through the direct transition of the nucleus from an initial state to a final state Ψi Ψ f , in time t, is given by (47.7) P t a tif f( ) | ( )|= 2 where the wave function amplitudes a are obtained from Eq.(37.11), which can be approximated by tf ( ) == /)()()()( tifiif ifetVtadt tda i εε −= (47.8) Since the probability of finding our decaying system in the initial state Ψi must decrease with time according to the radioactive decay law (47.3), which gives 2 2| ( ) | | | ti it e λ−Ψ = Ψ (47.9) we have to choose / 2( ) tia t e λ−= (47.10) rather than as considered in Eq.(37.13). Substituting this result into Eq.(47.8), and assuming a constant perturbation which is switched on at time t = 0, yields ai = 1, i εελ −+−= (47.11) Integrating, we get an oscillatory behaviour of the wave function amplitude, given by ( ) ( ) /2 V e a t i ε ε λ − +⎡ ⎤−⎣ ⎦= − + = == = (47.12) Figure 47.1. Energy spectrum of a decaying state of width Γ At the end of the nuclear transition we should consider the amplitude corresponding to ,∞→t which reads )( λεε = = i V a if fi f +−=∞ (47.13) and this yields the transition probability (47.7) in the form )( || )( Γ+−=∞ if fi if V P εε = (47.14) Hence, the probability to observe the nucleus with energy fε in the vicinity of iε follows a Lorentzian distribution, illustrated in Figure 47.1. By analogy with the atomic transitions, Γ = = 〈 〉= =λ / t gives the natural linewidth of the emitted radiation, which is the same as the width of the decaying nuclear state. Nuclear states which are populated in ordinary decays typically have lifetimes greater than corresponding to sec,10 12− ( ) τ/1066.0eV 15−×=Γ (47.15) which is of the order of Since this width is small compared with the energy spacing of nuclear levels, which is of the order of the nuclear decaying states may be regarded to be discrete quasi-stationary states.
According to theories of classical physics, a moving particle cannot move to an environment with greater potential energy than its total energy during movement. But according to quantum theories, this event is known to be. This event is called tunneling. Tunneling is a probability, and it is measured by transition coefficient. Correct calculation of this coefficient is particularly important because extremely sensitive and important instruments have been developed based on this event, and many events in nature can be explained by tunneling. This coefficient was generally calculated by semi-classical approaches (WKB) and the known formula is an approximate formula. In the previous papers, the general transmission coefficient of a potential barrier with arbitrary form is calculated by a simple method without any approximation. The results were applied to calculate the half-life values of the nuclei that emit alpha particle. In this article, the half-life calculation formulas obtained in previous studies were made simpler. It has been shown that it is applicable to all radioactive decays (alpha, beta, gamma etc.). The half-life values obtained from our calculations have been compared with the experimental values, and it has been found that the new half-life values are exactly consistent with the experimental values.
In the recent theory of radioactive decay, and also, as is shown, in the theory of dissociation of a diatomic molecule by the acquisition of rotational energy, there occurs a potential energy curve which has the following shape, as we go, say, from left to right. At the left the potential energy is very high, it then comes down to a minimum, increases to a maximum, and again falls off to an asymptotic value. The problems connected with such a curve are of two types. First, we may be given a particle in the region near the minimum, in an energy level which lies below the maximum, and wish to find the chance that it appear by a quantum mechanical process in the region on the other side of the maximum. Second, we wish to find how the "discrete states" in the neighborhood of the minimum are "broadened" by the continuum on the other side of the maximum. To solve these problems we first find the stationary eigenfunctions. By means of them the width and shape of the "broadened discrete levels" are found immediately. We then use these eigenfunctions to set up a wave packet, or, rather, we show how nature may set up a wave packet, which enables us to solve the first of the problems mentioned. The result justifies the use of complex eigenvalues for the solution of the problem.
Originally introduced in Schrödinger's Cat as “a tiny amount,” we generalize this concept and introduce Schrödinger's quantity, a measure of radioactivity from the beginning to the first decay occurrence, or the starting point of radioactive decay. Schrödinger's quantity describes the radioactivity of a given radioactive isotope by the amount, or number of atoms, corresponding to a one-half probability that a decay occurs during one half of the isotope's half-life, whereas half-life measures radioactivity from the beginning to the midpoint of radioactive decay.
The halflife of αradioactive elements has already been measured out through experiments. But, classical theory's failure to explain the phenomenon of αDecay is found in this article according to the analysis of the mechanism of αDecay. And in this article, this problem is completely settled through introducing of the theory of quantum tunneling effect yet. Furthermore, the halflife of αDecay of238U is illustrated and figured out with this theory, and is approximately in accordance with the figure of experiments.