scholarly journals q-Calculus and the Symmetrized Radioactive Decay Law

2021 ◽  
Author(s):  
Shawn Eastmond
Keyword(s):  
Radiocarbon Dating ◽  
Decay Constant ◽  
Radioactive Decay ◽  
Logarithmic Function ◽  
Ernest Rutherford ◽  
Exponential Form ◽  
Quantum Calculus ◽  
Label Method ◽  
Frederick Soddy ◽  
Q Values

The radioactive decay law was first formulated by Ernest Rutherford and Frederick Soddy in 1902. As a well-known law, one of its primary applications is to determine the dates of ancient specimens. The process is known as radiocarbon dating and is subjected to the known properties of radioactive nuclei. In this paper, we implement quantum calculus to express the solution of the radioactive decay equation in symmetrized q-exponential form. Also, we explore a q-analog of the decay constant using Tsallis logarithmic function for various miscellaneous q-values. Furthermore, the factor-label method was applied to our analysis to show that the correct units remained intact under the application of quantum calculus. In conclusion, our work suggests that a variation of the q-parameter was akin to the production of a new isotope for all q in (0,1); the superadditive regime.

scholarly journals A new continuous entropy function and its inverse

2011 ◽  
Vol 9 (1) ◽  
pp. 65-70
Author(s):  
Andrej Grebenc
Keyword(s):  
Differential Equation ◽  
Neural Networks ◽  
Economic Modeling ◽  
Integral Solution ◽  
Entropy Function ◽  
Lambert W Function ◽  
Logarithmic Function ◽  
Lebesgue Integral ◽  
Parametric Function ◽  
Exponential Form

A new continuous entropy function of the form h(x)=-k?p'(x)*ln(p(x)) is constructed based on Lebesgue integral. Solution of the integral is of the form h(x)=-k*p(x)*ln(e-1*p(x)). Inverse solution of this function in the form of p(x)=h(x)*W-1(h(x)* e-1) has been obtained and this is a novelty. The fact that the integral of a logarithmic function is also a logarithmic function has been exploited and used in a more general ansatz for a deliberate function. The solution of the differential equation ?(x)= g(x)'*ln(g(x)) for a deliberate function g(x) includes the Lambert W function. The solution is a parametric function g(x)=(s(x)+C)/W(e-1*(s(x)+C)). Parameter C has a minimal value and, consequently, an infimal function g(x) exists. This transform is of general use, and is particularly suitable for use in neural networks, the measurement of complex systems and economic modeling, since it can transform multivariate variables to exponential form.

6. Physics invades the periodic table

2019 ◽  
pp. 73-84
Author(s):  
Eric R. Scerri
Keyword(s):  
Nuclear Structure ◽  
Atomic Number ◽  
Periodic Table ◽  
Atomic Weight ◽  
Ernest Rutherford ◽  
Frederick Soddy ◽  
The Impact

‘Physics invades the periodic table’ assesses the impact of key discoveries in physics on the understanding of the periodic table. Ernest Rutherford provided evidence for the nuclear structure of atoms, and also determined that the charge of an atom is equal to half its atomic weight. Anton van den Broek linked this principle to the number of protons in a nucleus, thus devising the notion of atomic number. Henry Moseley quantified this principle, and used it to show exactly how many elements would fill the gaps in the periodic table. Radioactive experiments created new forms of elements with different weights but the same charge, which Frederick Soddy identified as isotopes.

The Suicidal Success of Radiochemistry

1979 ◽  
Vol 12 (3) ◽  
pp. 245-256 ◽  
Author(s):  
Lawrence Badash
Keyword(s):  
Physical Properties ◽  
Alpha Particle ◽  
Half Life ◽  
Periodic Table ◽  
Presidential Address ◽  
British Association ◽  
Experimental Science ◽  
Ernest Rutherford ◽  
Laboratory Bench ◽  
Frederick Soddy

In his presidential address to the chemistry section of the British Association in 1907, Arthur Smithells pointed to work in radioactivity with wonder, calling it the ‘chemistry of phantoms’. Indeed, the transitory nature of the radioelements, coupled with the exceedingly small quantities commonly handled, made many a traditional chemist hesitant to accept these unusual substances as real elements worthy of insertion into the periodic table. Besides, there were too many of them: by 1913 over thirty radioelements were known, but there were no more than twelve boxes in the periodic table in which to house them. Moreover, there was much confusion about radioelements that had different physical properties such as half-life and range of emitted alpha particle, but which could not be separated chemically. Small wonder then that Alexander Russell, the only person who worked with both Ernest Rutherford and Frederick Soddy, recalled the prevalent attitude of chemists as discouraging of interpretative attempts: theirs was, so they claimed, ‘an experimental science. No good ever came from pontificating on the ways of Nature from the comfort of an armchair. The laboratory bench, not the sofa, … was where the truth would be found’.

Pressure Dependence of the Radioactive Decay Constant of Beryllium-7

Science ◽  
1973 ◽  
Vol 181 (4105) ◽  
pp. 1164-1165 ◽  
Author(s):  
W. K. Hensley ◽  
W. A. Bassett ◽  
J. R. Huizenga
Keyword(s):  
Pressure Dependence ◽  
Decay Constant ◽  
Radioactive Decay

Radiocarbon dating

1970 ◽  
Vol 269 (1193) ◽  
pp. 1-10 ◽  
Keyword(s):  
Carbon Dioxide ◽  
Cosmic Rays ◽  
Radiocarbon Dating ◽  
Sea Water ◽  
Radioactive Decay ◽  
Cosmic Ray ◽  
Carbon 14 ◽  
Living Things ◽  
Long Time ◽  
Life On Earth

The cosmic ray production of new atoms in m atter is the basis of radiocarbon dating. In this case the atom is carbon of mass fourteen made from the most abundant atom in air—nitrogen of mass fourteen. Radiocarbon— carbon-14, 14 C—lasts 8300 years on the average (see note on radioactive decay on p. 10 for explanation of ‘half life’ and ‘average life’) before reverting in radioactive decay to nitrogen-14 and during this time it enters all living things as well as sea water and air. Chemically carbon dioxide (the product of the combustion of carbon with air—which is 20% oxygen) is the food of life and presumably the freshly produced 14 C atom burns sooner or later (probably in a few days, although this time is not at all well known) to 14 CO 2 a which is mixed with the ordinary carbon dioxide (0.03% in air) which contains mainly non-radioactive carbon atoms of masses 12 and 13 in abundances of 99% and 1%, respectively. The process which converts CO 2 a into plants—photosynthesis—is the way in which the radio­ carbon is introduced into living beings, for all life on Earth so far as is known either is a plant or lives off plants. In principle and in theory one could understand if organisms were to live off fossil (or primeval, if there be any) organic matter and that radiocarbon dating would not work for them. They would not be in touch with the cosmic rays through recent photosynthesis and the long time that coal or oil has been underground would have required that the original radiocarbon (assuming the cosmic rays were working when the coal and oil deposits were made) would long since have disappeared.

Frederick Soddy and the Practical Significance of Radioactive Matter

1979 ◽  
Vol 12 (3) ◽  
pp. 257-260 ◽  
Author(s):  
Michael I. Freedman
Keyword(s):  
Research Programme ◽  
First World War ◽  
Practical Significance ◽  
World War ◽  
Ernest Rutherford ◽  
Frederick Soddy ◽  
The First World War ◽  
The University ◽  
First World ◽  
Scientific Achievements

It is for his scientific achievements that we best remember Frederick Soddy—first as the young chemist working with Ernest Rutherford and with William Ramsay in elaborating the disintegration theory of radioactive change, and then as the mature chemist, heading a research programme of his own at the University of Glasgow, a programme which culminated in his formulation of the concept of isotopes in the years before the First World War. Yet there was another side to Soddy's early scientific career: beyond his profound concern with the purely theoretical and experimental aspects of radioactivity research, there was a serious interest in what might be called the practical significance of his science. By practical, I mean those aspects capable of being put to use for the immediate or potential future benefit of man. In this paper I wish to elucidate the nature of this concern during Soddy's career, focusing particularly upon his years at the University of Glasgow, 1904–1914.

scholarly journals Determining the Half Time and Analogy Constants of Radioactive Decay on the Illustration Board of Radioactive Decay with the Capacitor Filling and Discharging Method

2019 ◽  
Vol 7 (3) ◽  
pp. 306-316
Author(s):  
Anggi Julvian Rachma ◽  
Delia Achadina Putri ◽  
Maria Ulfah ◽  
Dandan Luhur Saraswati
Keyword(s):  
Experimental Data ◽  
Half Life ◽  
Decay Constant ◽  
Radioactive Decay ◽  
Radioactive Substance ◽  
Half Time ◽  
Radioactive Elements ◽  
Decay Constants ◽  
Significant Difference ◽  
Very High

Radioactive decay is one of the material to be learned students in the study of physics. However, until now students only learn concepts through existing teaching materials. This is because, the level of danger is very high if students have to deal with radioactive elements. So, it does not allow students to experiment with decay directly. Through an illustration board of radioactive decay, students can learn radioactive decay events by illustrating radioactive decay by capacitor filling and emptying methods. In addition, through this props, students can determine the value of the decay constant and the half-life of a radioactive substance. Based on the results of experiments using capacitors (C) of 4700 μF and resistors (R) of 56 kΩ, the percentage of theoretical experimental data deviation is 2.63% for decay constants, and 3.06% for half-life. This illustrates that there is no significant difference from the theoretical experimental data. So, it can be concluded that the illustration board of radioactive decay is suitable to be used as an illustration tool for radioactive decay events and determine the value of the characteristics of radioactive decay (decay constant and half-life).Keywords: Props, Radioactive Decay, Half-Life, Decay ConstantPeluruhan radioaktif merupakan salah satu materi yang harus dipelajari siswa dalam bidang studi fisika. Namun, sampai saat ini siswa hanya mempelajari konsep melalui bahan ajar yang ada. Hal tersebut dikarenakan, tingkat bahaya yang sangat tinggi jika siswa harus berhadapan dengan unsur radioaktif. Sehingga, tidak memungkinkan siswa melakukan percobaan peluruhan secara langsung. Melalui alat illustration board of radioactive decay, maka siswa dapat mempelajari peristiwa peluruhan radioaktif melalui pengilustrasian peluruhan radioaktif dengan metode pengisian dan pengosongan kapasitor. Selain itu, melalui alat peraga ini siswa dapat menentukan nilai konstanta peluruhan dan waktu paruh dari suatu zat radioaktif. Berdasarkan hasil percobaan dengan menggunakan kapasitor (C) sebesar 4700 μF dan resistor (R) sebesar 56 kΩ, diperoleh persentase penyimpangan data percobaan dengan teoritis sebesar 2,63% untuk konstanta peluruhan, dan 3,06% untuk waktu paruh. Hal tersebut menggambarkan bahwa tidak terdapat perbedaan yang signifikan dari data hasil percobaan dengan teoritis. Sehingga, dapat disimpulkan bahwa alat illustration board of radioactive decay cocok untuk dijadikan alat ilustrasi peristiwa peluruhan radioaktif dan menentukan nilai karakteristik peluruhan radioaktif (konstanta peluruhan dan waktu paruh).Kata kunci: Alat Peraga, Peluruhan Radioaktif, Waktu Paruh, Konstanta Peluruhan

Meteorite Phosphates Show Constant 176Lu Decay Rate Since 4557 Million Years Ago

Science ◽  
2005 ◽  
Vol 310 (5749) ◽  
pp. 839-841 ◽  
Author(s):  
Yuri Amelin
Keyword(s):  
Decay Rate ◽  
Decay Constant ◽  
Radioactive Decay ◽  
Ordinary Chondrite ◽  
The Earth ◽  
Isotopic System

The use of radioactive decay of 176Lu to 176Hf to study the evolution of the Earth requires a precise and accurate value for the 176Lu decay constant. Recent determinations of this decay constant by age comparison to the more precisely calibrated U-Pb isotopic system produced internally consistent but discrepant values between terrestrial minerals and meteorites. New highly radiogenic Lu-Hf data for phosphate minerals from Richardton (ordinary chondrite) and Acapulco (primitive achondrite) yield decay constant values of 1.864 × 10–11 ± 0.016 × 10–11 and 1.832 × 10–11 ± 0.029 × 10–11 year–1, respectively, identical to the value determined from terrestrial minerals.

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