Nuclear Size and Density

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Nuclear Size and Density

A2 lecture


Electron scattering

• The most definitive information about nuclear sizes comes from electron scattering.


Mass radius and charge radius

Comparisons of calculated and experimental radii for nuclei have made it clear that there is a "tail" where the density of nuclear matter decreases toward zero.

• The nucleus is not a hard sphere. • The evidence points to a mass radius

and a charge radius which agree with each other within about 0.1 fermi.


Fermi Model

• Various types of scattering experiments suggest that nuclei are roughly spherical and appear to have essentially the same density.

• The data are summarized in the expression called the Fermi model: where r is the radius of the nucleus of mass number A.


Constant nuclear density

• The assumption of constant density leads to a nuclear density value of


Dense material!

• The nuclear radius is less than 0.01 % (1/10,000th) of the radius of the atom. Thus the density of the nucleus is more than a trillion times that of the atom as a whole.

• One solid cubic millimeter of nuclear material, if compressed together, would have a mass of around 200,000 tonnes.

• Neutron stars are composed of such material.


Calculations

Use the density and the nucleon number (mass number) of the following isotopes to work out the nuclear radius of the following atoms.

(a) Uranium 235(b) Carbon 12(c) Helium 4


Calculation Answers

(a) Uranium 235 - 7.41 x 10-15m(b) Carbon 12 - 2.74 x 10-15m(c) Helium 4 - 1.90 x 10-15m


Relative scale model of an atom and the solar system

• If we scaled a gold nucleus to be about a foot in diameter and then did the same with the Sun we get a surprising result.


Nuclear Density and the Strong Force

• The fact that the nuclear density seems to be independent of the details of neutron number or proton number implies that the force between the particles is essentially the same whether they are protons or neutrons.


Nuclear Density and the Strong Force

• This correlates with other evidence that the strong force is the same between any pair of nucleons.


Nuclear Forces

• Within the incredibly small nuclear size, the two strongest forces in nature are pitted against each other.

• When the balance is broken, the resultant radioactivity yields particles of enormous energy.


Strong force

• The electron in a hydrogen atom is attracted to the proton nucleus with a force so strong that gravity and all other forces are negligible by comparison.

• But two protons touching each other would feel a repulsive force over 100 million times stronger!!

• So how can such protons stay in such close proximity?

• This may give you some feeling for the enormity of the nuclear strong force which holds the nuclei together.


Balance of forces


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Nuclear Size and Density