https://wiki.nivel-teorico.com/index.php?action=history&feed=atom&title=Dispers%C3%A3o_de_RutherfordDispersão de Rutherford - Histórico de revisões2026-04-20T21:56:32ZHistórico de edições para esta página nesta wikiMediaWiki 1.40.1https://wiki.nivel-teorico.com/index.php?title=Dispers%C3%A3o_de_Rutherford&diff=6179&oldid=prevCalimero0000: uma edição2013-05-03T11:42:17Z<p>uma edição</p>
<p><b>Página nova</b></p><div>Em [[física]], a '''dispersão de Rutherford''' é um fenômeno que foi explicado por [[Ernest Rutherford]] em [[1909]],<ref>E. Rutherford, "The Scattering of α and β Particles by Matter and the Structure of the Atom", Philos. Mag., vol 6, pp.21, 1909</ref> e levou ao desenvolvimento da [[Átomo de Bohr|teoria orbital]] do [[átomo]]. É agora explorado pela técnica de análise de materiais [[espectrometria de dispersão de Rutherford]]. A dispersão de Rutherford é também referida às vezes como '''dispersão de Coulomb''' porque baseia-se em [[força]]s [[eletricidade estática|eletrostáticas]] ([[Coulomb]]). Um processo similar provou o interior do núcleo nos anos 1960, chamado [[dispersão profunda inelástica]].<br />
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The discovery was made by [[Hans Geiger]] and [[Ernest Marsden]] in [[1909]] when they performed the [[Geiger-Marsden experiment|gold foil experiment]] under the direction of Rutherford, in which they fired a beam of [[alpha particle]]s ([[helium]] nuclei) at layers of [[gold]] leaf only a few atoms thick. At the time of the experiment, the atom was thought to be analogous to a plum pudding (as proposed by [[J.J. Thomson]]), with the negative charges (the plums) found throughout a positive sphere (the pudding). If the [[plum-pudding model]] were correct, the positive “pudding”, being more spread out than in the current model of a concentrated [[atomic nucleus|nucleus]], would not be able to exert such large coulombic forces, and the alpha particles should only be deflected by small angles as they pass through.<br />
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However, the intriguing results showed that around 1 in 8000 alpha particles were deflected by very large angles (over 90°), while the rest passed straight through with no deflection. From this, Rutherford concluded that the majority of the [[mass]] was concentrated in a minute, positively charged region (the nucleus) surrounded by electrons. When a (positive) alpha particle approached sufficiently close to the nucleus, it was repelled strongly enough to rebound at high angles. The small size of the nucleus explained the small number of alpha particles that were repelled in this way. Rutherford showed, using the method below, that the size of the nucleus was less than about 10<sup>&minus;14</sup> m (how ''much'' less than this size, Rutherford could not tell from this experiment alone; see more below on this problem of lowest possible size).<br />
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== Seção transversal diferencial ==<br />
[[Ficheiro:ScatteringDiagram.svg|thumb|right|250px|Dispersão repulsiva por uma partícula pontual.]]<br />
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Como derivada por Rutherford em 1911, a seção transversal diferencial é<br />
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::<math>\frac{d \sigma}{d \Omega} = \left(\frac{\alpha \hbar c}{2mv_0^2} \right)^2 \frac{1}{\sin^4 (\theta / 2)}</math><br />
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Todas as partículas que atravessam o anel à esquerda terminam em algum lugar acima no anel à direita.<br />
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== Details of calculating maximal nuclear size ==<br />
For head on collisions between alpha particles and the nucleus, all the [[kinetic energy]] (<math>\begin{matrix}\frac{1}{2}mv^2\end{matrix}</math>) of the alpha particle is turned into [[potential energy]] and the particle is at rest. The distance from the centre of the alpha particle to the centre of the nucleus (''b'') at this point is a maximum value for the radius, if it is evident from the experiment that the particles have not hit the nucleus.<br />
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Applying the [[inverse-square law]] between the charges on the electron and nucleus, one can write:<br />
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<center><math>\frac{1}{2} mv^2 = \frac{1}{4\pi \epsilon_0} \cdot \frac{q_1 q_2}{b}</math></center><br />
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Rearranging:<br />
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<center><math>b = \frac{1}{4\pi \epsilon_0} \cdot \frac{2 q_1 q_2}{mv^2}</math></center><br />
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For an alpha particle:<br />
* '''m''' (mass) = 6.7×10<sup>&minus;27</sup>&nbsp;kg<br />
* '''q<sub>1</sub>''' = 2×(1.6×10<sup>&minus;19</sup>)&nbsp;C<br />
* '''q<sub>2</sub>''' (for gold) = 79×(1.6×10<sup>&minus;19</sup>)&nbsp;C<br />
* '''v''' (initial velocity) = 2×10<sup>7</sup>&nbsp;m/s<br />
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Substituting these in gives the value of about 2.7×10<sup>&minus;14</sup>&nbsp;m. (The true radius is about 7.3×10<sup>&minus;15</sup>&nbsp;m.) The true radius of the nucleus is not recovered in these experiments because the alphas do not have enough energy to penetrate to more than 27 fm of the nuclear center, as noted, when the actual radius of gold is 7.3 fm. Rutherford realized this, and also realized that actual impact of the alphas on gold causing any force-deviation from that of the 1/r coulomb potential would change the ''form'' of his scattering curve at high scattering angles (the smallest impact parameters). This was not seen, indicating that the gold had not been "hit" so that Rutherford only knew the gold nucleus (or total of gold and alpha radius) was smaller than 27 fm (2.7×10<sup>&minus;14</sup>&nbsp;m)<br />
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In 1919, a very similar experiment in Rutherford's laboratory showed departures from Coulombic scattering from different energy alphas on hydrogen nuclei, with a departure radius (indicating a true "collision" or change in force characteristics) occurring at about a calculated impact parameter or closest approach of 3.5 fm. Further investigations of alpha scattering on nitrogen and oxygen in Rutherford's laboratory convinced Chadwick and others by 1921 that at these scales and energies, forces which were other than simple coulomb repulsive forces were at work in close nuclear interactions.<ref>See pg. 239, Abraham Pais, '''Inward Bound'''Oxford University Press, 1986, ISBN 0-19-851971-0</ref><br />
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== Other applications ==<br />
The principle of Rutherford scattering is now routinely used<br />
in [[Rutherford backscattering]] spectroscopy (RBS) to detect heavy<br />
elements in a lower atomic number matrix, like for example heavy<br />
metal impurities in semiconductors. In fact, the technique was also<br />
the first local analytical technique applied on the moon, as an RBS<br />
experiment was in place to take data when the Surveyor mission<br />
impacted the lunar surface.<br />
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{{Referências}}<br />
* E. Rutherford, [http://www.lawebdefisica.com/arts/structureatom.pdf ''The Scattering of α and β Particles by Matter and the Structure of the Atom], Philosophical Magazine. Séries 6, vol. '''21'''. maio 1911<br />
* H. Geiger and E. Marsden, [http://dbhs.wvusd.k12.ca.us/webdocs/Chem-History/GM-1909.html ''On a Diffuse Reflection of the α-Particles], Proceedings of the Royal Society, 1909 A vol. '''82''', p.&nbsp;495-500<br />
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== {{Ver também}} ==<br />
* [[Colisão de Coulomb]]<br />
* [[Teoria da dispersão]]<br />
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{{Portal3|Física}}<br />
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