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CHAPTER 1

Elements of Nuclear physics

Robert EshunS.L.T. Department ACCRA POLYTECHNIC

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Alpha scattering experiment

Plum pudding model of the atom.

Description of the set-up of the alpha scattering experiment.

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A zinc sulfide screen (a scintillator) placed behind the foil as a backdrop for the alpha particles to appear upon.

A microscope directly positioned above this screen to observe any contact made between the alpha particles and the screen.

Fast moving beam of alpha particles fired through a thin gold foil.

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ObservationsA large majority of alpha particles passed straight through

the foil.

A hand full of particles deflected slightly from the straight path by about one or two degrees.

A fewer number of particles were deflected approximately 90 degrees or more from the incident beam.

Occasionally, some particles were deflected back at the experimenter (180 degree deflection).

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From J.J. Thomson’s model of an atom, the alpha particles should have passed directly through the gold foil in every attempt.

Few deflections observed which could not be explained with the Thomson model.

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Deductions

Particles which were not deviated were not incident on or come close to any positive charge.

Those which were deviated might have come close to a large positive charge, with those that went closest deviated over large angles.

Particles which were reflected back along the same path were directly incident on a large positive charge.

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The results of the experiment led to two conclusions:

An atom was much more than just empty space and scattered electrons and

An atom must have a positively charged centre that contains most of its mass (which Rutherford termed as the nucleus).

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Rutherford’s model

A massive, central positive nucleus, about ten thousand times smaller than the atom as a whole (in terms of volume). ...

Surrounded by negatively charged orbiting electrons.

The nucleus contains nearly all of the mass of the atom, but it occupies only a tiny fraction of the space inside the atom.

Most of the mass of the atom was contained in the nucleus, and that the rest of the atom was mostly empty space.

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Distance of closest approach

As alpha particles approach a nucleus they are repelled.

As they approach the nucleus their kinetic energy is changed into potential energy as the particles get closer and slow down.

For head-on approach, as they get closer to the nucleus they get slower until they finally stop, and reverse as they are repelled backwards.

The distance between the point where a particles stops and the nucleus is known as the distance of closest approach.

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Alpha particle (+2e)

Gold nucleus (+79e)

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The problem with the Rutherford model is that:

The nucleus and its orbiting electrons are oppositely charged, and therefore attract one another.

Nothing should stop the electrons from being pulled immediately into the nucleus.

Therefore atomic matter is expected to implode immediately they were created.

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Also, Rutherford's model contains accelerating charges and are to radiate energy according to classical physics.

This implies that the electrons will spiral down into the nucleus as they lose energy through radiation

This probably leads back to the plum pudding (Thomson’s) model.

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Bohr’s modelBohr’s postulates:

Postulate 1: An electron in an atom moves in a circular orbit about the nucleus under the influence of the Coulomb attraction between the electron and the nucleus, obeying the laws of classical mechanics.

Postulate 2: Instead of the infinite number of orbits which would be possible in classical mechanics, it is only possible for an electron to move in an orbit for which its orbital angular momentum L is an integral multiple of .

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Postulate 3: Despite the fact that it is constantly accelerating, an electron moving in a specified or allowed energy level (orbit) does not radiate electromagnetic energy. Thus, its total energy E remains constant.

Postulate 4: Electromagnetic radiation is emitted by an electron only when it moves from a higher energy level to a lower one.

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Use postulates to derive total energy of an electron in an orbit.

Atomic SpectraWhen an atom absorbs energy, its electrons get excited

and moved to higher energy levels (or orbits).

Specific amounts or quanta of energy are absorbed to move from lower to higher orbital ...

or emitted when moving from higher to lower orbital.

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High p.d. established across the electrodes of a discharge tube containing a gas, excites some electrons in the atoms of the gas to higher energy levels.

When excited electrons move back to lower energy levels, they give off energy corresponding to the difference in energy between the two levels involved.

This excess energy is seen as a spectrum.

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Every possible transition in a given atom corresponds to a particular energy value, so different lines are observed corresponding to different wavelengths.

Derive relationship between wavelength (frequency) and principal quantum number to show that the wavelength given off is quantised.

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The wavelengths are in groups or series depending on the final energy level of the transitions involved.

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Flaws in Bohr’s theory

The theory is an uneasy mix of classical and quantum-mechanical ideas.

The electron travels in a classical orbit, and yet its angular momentum is quantized, contrary to classical mechanics.

The electron obeys Coulomb's law of classical electromagnetic theory, and yet it is assumed to not radiate, as it would classically.

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It does a good job of predicting energy levels, but does not predict transition rates between levels.

Finally, the theory only works soundly for the hydrogen atom, but fails even for helium.