Electron Scattering - The Nucleus
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A laser is shone on a pinhead and this diffraction pattern is produced. Just like a circular aperture, a spherical object can also produce a diffraction pattern if the wavelength of the radiation is small enough. |
In the Quantum Physics section we saw how electrons, with about 500eV of energy, could behave as waves as they were diffracted by the carbon atoms in graphite. We also saw how their wavelength depended on their momentum.
If we have electrons with sufficient momentum their wavelength may be small enough to be diffracted by atomic nuclei. Electrons from a particle accelerator, with about 500MeV of energy, are used to do this.
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Electrons whiz past the nuclei and are scattered. This is
the graph we get of number of electrons against the angle from the
straight through position.
Notice there is a dip in the graph. This minimum is due to diffraction effects. We can measure the angle of this dip and use it to calculate the radius of the target nuclei using the formula sin Ømin = 1.2 L / b where L is the De Broglie wavelength of the electrons and b is the diameter of the nuclei. Remember L = h / mv where h is Plank's constant. |
Now we have an accurate way of measuring the radii of nuclei.
An interesting relationship is found if we plot the nucleon number A of nuclei against their radii cubed.
This is more significant than it may first appear. It means that all nuclei, whether big or small, have the same density.
There is a very useful analogy we can use called the water drop model.
Water drops also all have the same density.
Their stability is governed by surface tension effects so small ones tend to stick together and large ones tend to break apart.
If A is proportional to r3 then r = k A 1/3 . Now if A = 1 then k is the radius of a single nucleon, i.e. a proton or neutron. So, r = ro A 1/3
The gradient of a graph of r against A 1/3 gives us a value for r0, the radius of a proton, of about 1 x 10-15m.
What holds nuclei together?
The electrostatic repulsive force between two protons very close together is enormous.
The force holding them together is called the "strong nuclear force".
It is strong. It has to be to hold protons together.
It acts on protons and neutrons. Perhaps this is why nuclei need neutrons, to provide enough strong force to hold them together. As nuclei get bigger they need more and more neutrons to be stable.
It has a very short range. Nucleons only attract their nearest neighbors. If this were not the case then larger nuclei would be pulled together more than they are and would be denser, which we know they're not.
