Question

rutherford soddy law

Answer 1

HEY
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the law of Rutherford and Soddy give is
radioactive material
The formulation of the radioactive decay law, in 1902, by Ernest Rutherford (1871–1937) and Frederick Soddy (1877–1956) was part of a number of discoveries around the turn of the century, which paved the way to the establishment of quantum mechanics, as the physics of the atom. In November 1895, W. Röntgen (1845–1923) discovered ► X-rays; in 1896 A. H. Becquerel (1852–1908) discovered radioactivity during an investigation of phosphorescence in uranium salts; finally in 1897 J.J. Thomson (1856–1940) discovered the ► electron. Rutherford and Soddy based their formulation of the radioactive law on the ‘emanation theory’ of radioactive decay. According to this theory, radioactivity is an ‘atomic’ phenomenon, which is accompanied by ‘chemical’ changes. Note that in 1902, Rutherford had not yet inferred from large-angle ► scattering experiments that the atom had a nucleus (► Rutherford atom). One chemical element, Rutherford and Soddy explained, was transformed into another by emitting charged particles: α-particles or β-particles. Around that time Rutherford already knew that radioactivity manifested itself in the form of ‘alpha rays’ or ‘beta rays’, which proved to consist of particles. Prior to his discovery of the nucleus model of the atom (1911), Rutherford regarded alpha particles as ionized helium atoms. α-particles are helium nuclei with an exit velocity of approximately 107m s−1 (with energies ranging between 4–9 MeV) and positive charge so that they experience deflections in electric and magnetic fields. β-particles are ► electrons with emission velocities, which range between 108ms−1 and 0.999c, and negative charge so that they, too, experience deflections in electric and magnetic fields. (Beta decay reveals a continuous energy spectrum up to a maximum E 0, depending on the type of nucleus involved; the kinetic energy Q can range from a few keV into the region of MeV.) Rutherford and Soddy emphasized that the ‘chemical’ changes had their seat within the atom and not on the molecular level. Today radioactivity denotes the ability of certain nuclei to undergo transformations through the emanation or emission of radiation. (Rutherford and Soddy were aware that this process can include γ-radiation — light of very short wavelength —, which is not deflected in electric or magnetic fields.) Rutherford and Soddy could not say what caused the emission of the subatomic particles from the atomic nuclei. The radioactive elements, their theory stipulated, ‘must be undergoing spontaneous transformation’ [1, 493]. In terms of the classical notion of determinism, the emanation theory did not permit the precise prediction of the time and trajectories of emitted particles. The theory was based on the formulation of statistical laws, which give rise to ► indeterminism.

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Answer 2

Rutherford Soddy law

The law states that number of nuclei disintegrating per second of a radioactive sample is directly proportional to the number of  nuclei  that has not decayed in the sample at that instant.

The proportionality constant is symbolized by the Greek letter lambda (λ)is called the decay constant.

If N is the number of nuclei present at a given time  and $\frac{dN}{dt}$ is the rate of decay after a particular time then according to law,

$-\frac{dN}{dt}$∝$N$

$-\frac{dN}{dt} =$λ$N$

$-dN=$λ$Ndt$

$-\frac{dN}{N} =$λ$dt$

Integrating from  $N_{0}$ to $N$ on left hand side and integrating from $0$ to $t$ on the right hand side we get;

$N=N_{0}e^{-lambda*t}$

N$=$number of radioactive nuclei present

$N_{0} =$initial number of radioactive nuclei

lambda(λ)$=$decay constant

$t=$time taken for decay

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