# The scale of the matter in different levels

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The scale of the matter in different levels The experimental technique of deep inelastic scattering has revealed to understand the most basic structure of matter

1.6 Atomic structure: The “plum-pudding” model (ca Thomson) imagined electrons embedded in a jelly-like positive medium. Rutherford proposed a “planet model” or Rutherford model Rutherford, Geiger & Marsden found that -particles fired at a thin gold foil occasionally scattered backwards.

Discovery of the electron
In the late 1800s several experiments were performed on electrical discharges in gases at low pressure. It was established that a stream of some kind of “rays” – called cathode-rays – was emitted by any electrode at high negative potential in a vacuum tube. What were these rays? Gas discharge tube

Discovery of the electron
J. J. Thomson clarified the situation with a decisive experiment. Particles have negative charge By measuring the deflection of these particles Thomson showed that all the particles have the same q/m ratio. Thomson also showed that particles with this q/m ratio can be obtained using any material as source – These particles – now called electrons – are a fundamental constituent of matter.

Thomson’s e/m experiment
Thomson found that in his experiment, the speed of the particles was extremely high – ~ 1/10 c Value of q/m =  104 C/kg Thomson was able to show that this new particle – the electron – with its absolutely characteristic charge-to-mass ratio was a constituent of every substance that he was able to use as a cathode material.

Millikan’s “Oil-drop” Experiment
Millikan’s oil-drop experiment demonstrated that electric charge is quantized and transferred in integral multiples of e. Millikan provided first crude measurement of e. We know now: e =  C. m =  g. It was supposed that the positive charges were heavier than the electrons – The hydrogen ion turned out to be 1836 times heavier than the electron.

Millikan’s “oil-drop” experiment
Experimental arrangement of Millikan. The oil droplets, which are formed by the atomiser, can be charged or discharged by irradiation with x-rays.

Plum-pudding model Atomic radii: R ~ 1 Å = 10-10 m
Thomson’s atomic model: Atom has to be electrically neutral. Thomson proposed an atomic model in which electrons were embedded in a massive matrix of positive charge filling a volume of roughly 1 atomic diameter (~ 1 Ao). This model is called the “plum-pudding” model in which the electrons are analogous to raisins in a plum pudding. e R electron R ~ m Positively charged matter Electrons are almost point charges Calculations based on classical E&M gives ro = e2/mc2 Radius of electron  2.8 X m

The nucleus of the atom

Cloud chamber pictures
wall Cloud chamber The track of alpha particle Cloud chamber photograph of the track of an alpha particle, by wilson. The particle passes through several cm of air without noticeable deflection. At the end of the track, we see two deflections; at the second, we can also see the short track of the target nucleus, which was accelerated to the right by the collision.

Cloud chamber pictures
H gas He gas deflection Supersaturation: To cause (a vapor) to exceed the normal saturation vapor pressure at a given temperature. Cloud chamber photograph of alpha particles. Left, the chamber gas is hydrogen. The alpha particle is only slightly deflected from a straght-line track, while the hydrogen nucleus recoils sharply off to the left. Right, it is helium. The angle between the tracks of the alpha particle and the recoiling nucleus after the collision is 900, since the two particles have the same mass.

Rutherford model of the atom
The most direct way of finding out what’s inside a fruitcake is to put a finger into it -- A method similar to that used by Geiger and Marsden in 1911. At the suggestion of Rutherford, they used as probes fast -particles emitted by certain radioactive elements - (-particles are helium atoms that have lost 2 electrons – charge +2e)

Rutherford scattering experiment
Radioactive substance that emits -particles -particles Thin metallic foil Microscope Zinc sulphide screen (gives off a green flash when struck by ) It was expected that  would go straight through the foil without deflection (follows from Thomson’s model) With only weak electric forces exerted on them  ought to deflect only slightly – 1o or less. G&M found that while most  were not deviated much, some scattered through very large angles. Some even scattered backwards!

Scattering by thin gold foils (on glass)
Measured a scattering through materials Rutherford and Geiger first measured scattering of a particles through the foils. With the thinnest foils, scattering was only 1 or 2 degrees. Undergraduate experiment for Ernest Marsden: “see if any alpha particles are scattered backward.” To Rutherford’s great surprise, there were indeed alphas scattered backward. He later said: “It was as incredible as if you fired a 15” shell at a piece of tissue paper and it came back and hit you!”. Scattering of  rays by an atom Setting of the experiment

Most of the  particles are pass through straight, part of them are scattered in large angles, even in backward.

Results of Rutherford scattering
Scattering angle  The experimental results of Geiger and Marsden for the Rutherford scattering of  particles by a gold foil. The scattering rate N is plotted as a function of the scattering angle . The solid curve represents the theoretical function for Coulomb scattering.

Rutherford model of the atom
Rutherford found – only way to explain results is to picture the atom as being composed of a tiny nucleus with the electron some distance away: + - Rutherford’s model Within an atom being mostly empty space, most  are undeflected. But, when  comes near nucleus, intense electric field cause it to be scattered through large angles – (E ~ 1021 V/m)

Rutherford model of the atom
All the atoms of any one element were found to have the same unique nuclear charge. — This charge increased regularly from element to element in the periodic table. Nuclear charge always turned out to be multiples of +e the number Z of the element. Ordinary matter, then, is mostly empty space. By considering only the Coulomb interaction between the incident  and the target nucleus, Rutherford calculated the scattering counts and obtained results which agreed remarkably well with experiments.

Rutherford, Ernest ( ) New Zealander-English physicist who was born in Nelson, New Zealand. Rutherford is best known for devising the names alpha, beta, and gamma rays to classify various forms of "rays" which were poorly understood at his time. Rutherford suggested that the simplest possible rays must be those obtained by hydrogen and that these must be the fundamental positively charged particle, which he dubbed the proton in In 1917, he passed alpha particles through a gas of nitrogen and occasionally observed scintillation of hydrogen impacting on his screen. He concluded that the alpha particles were knocking protons out of the nitrogen atoms, and thus that he had made the first observation of nuclear reactions. Rutherford's image appears on New Zealand's \$100 note, that country's largest denomination of paper currency. One particularly memorable quote attributed to Rutherford is "All science is either physics or stamp collecting“. In 1908 Rutherford was awarded the Nobel Prize – for Chemistry! The award citation read – “For his investigations into the disintegration of the elements and the chemistry of radioactive substances.”

Rutherford scattering
The repulsive Coulomb force:

Trajectories for Rutherford Scattering
12 10 8 6 4  particle 2 -θ0 b - 4 - 2 2 4 6 8

Derivation of Rutherford’s scattering formula
impact parameter Scattering angle  particle Rutherford's model enables us to derive a formula for the angular distribution of scattered a-particles. Basic Assumptions: a) Scattering is due to Coulomb interaction between a-particle and positively charged atomic nucleus. b) Target is thin enough to consider only single scattering (and no shadowing) c) The nucleus is massive and fixed. (This simplifies the calculation, but it could be avoided by working in the centre of mass frame). d) Scattering is elastic.

Relation between b and 

Differential cross section da:
Rutherford formula The incident  particles with impact parameters in the range b to b+db are deflected into the range of angles  to -d. Differential cross section da:

The Rutherford formula and the experimental results
The Rutherford formula has been experimentally tested with great care. Keeping the solid angle d constant, the sin-4(/2) law is found to be excellently reproduced in the counting rate. Even with the alpha particles of energy 5MeV and scattering angle of 1500, no deviations from the Rutherford formula are found; this corresponds to an impact parameter of 6×10-15 m. In this region, only the Coulomb potential of the nucleus has a measurable effect on the alpha particles. The nucleus radius is thus R < 6×10-15 m. From experiments with different foil materials, the nuclear charge Z can be determined. The experiments of Chadwick (1920) verified that Z is identified with the position of the element in the periodic table.

The anomalous Rutherford scattering
The scattering of very fast alpha particles ( E > 6MeV) at large angles , i.e., with small impact parameters b — nearly central collisions, clear deviations from the Rutherford formula, the sin-4(/2) law is never obeyed. The alpha particles approach the nuclei so closely, the short-range interaction force becomes more effective than Coulomb force. The nuclear force An alpha particle, which approaches a nucleus from outside the atom, is acted on at first only by the repulsive Coulomb potential. If it approaches the nucleus sufficiently closely, it will also be acted upon by the attractive nuclear force.

What is meant by nuclear Radius
Nuclear force and Coulomb potentials The nuclear Radius: the distance at which the effect of the nuclear potential is comparable to that of the Coulomb potential.

The empirical result of the nuclear Radius R and the mass number A:
R = (1.3 ± 0.1)A1/3 · m Numerical examples for A = 12 and A = 208:

Scattering processes play an important role in nuclear and elementary particle physics, in the investigation of the internal structure of nuclei and of certain elementary particles. For example, Hofstadter was granted the Nobel prize in 1961 for his scattering experiments using fast electrons ( 109 eV) on protons and neutrons. From the angular dependence of the scattering intensity, he was able to obtain information about the inner structure of the proton and of the neutron.

Homework: Pp48, problems 4.2, 4.3, 4.6, 4.8