Nuclear Size Exploration
The purpose of this exploration is to use Rutherford’s atomic theory to illustrate a gold
foil containing gold atoms and appreciate the fact that most incident alpha particles pass
straight through the foil. This simulation presents a visual model to help relate to the
experimental results of the Rutherford experiment.
As you work through this exercise, have the applet open in a separate window. (If
necessary click on the link, gold3d.swf) If you need help understanding the simulation
and controls, see the Help menu for assistance.
Gold Foil Model
In his famous scattering (gold-foil) experiment, Rutherford used a very thin sheet of pure
gold that was a few hundred atoms thick. In this computer model, this is simplified to just
three atoms thick. Click one of the “Rotate” buttons to view the layers of gold atoms of
this model. Notice that the atoms are tightly packed which is a characteristic of metal
structures.
A gold foil looks solid; however, according to the Rutherford atomic theory, the
individual atoms are composed of mostly empty space. This space contains the electrons
which are so small and widely dispersed that the alpha particle passes through
unhindered.
Nuclear Size
The key part of the Rutherford theory is that all of the positive charge and almost all of
the atom’s mass is concentrated in a tiny central structure called the nucleus. Because of
its charge and mass, the nucleus is the structure that affects the movement of the incident
alpha particle.
1. Click on the “Nuclei Only” button and the electron clouds will disappear leaving
only the nuclei. Can you see the dots representing the nuclei? Use the Zoom
control (up and down arrows or mouse scroll wheel) to adjust the zoom until you
can just barely see the dots. At what zoom factor is it possible to first see the
nuclei on the screen?
In reality, even this scale makes the nucleus’ size appear about 50X larger than it would
be with an atom of this size as represented on the screen.
2. Using modern values, the radius of a gold nucleus is 7 fm and the radius of a gold
atom is 135 pm. How many times larger is the atomic radius compared with the
nuclear radius?
Scattering
Reset the display so that you are viewing the gold foil head-on. Pretend you are an alpha
particle and zoom into the foil until you pass through. Reset the display and do this “fly
through” at different orientations of the gold foil. Note that you can use the arrows at the
edges of the screen to shift the model in various directions.
3. Although this is very approximate and qualitative, describe the chances of
zooming right into or very near the nucleus.
4. For the alpha particle to deflect strongly it has to pass within about six nuclear
radii from the nucleus. What is this distance in picometres for a gold atom? How
does this compare with the diameter of the gold atom?
Summary
The nucleus is extremely small relative to the size of the atom. As an analogy, the
nucleus would be a speck of dust centred within an atom the size of three football fields.
We cannot see the nucleus even with the most powerful microscopes. In spite of its small
size, the nucleus contains all of the positive charge in an atom as well as almost all of the
atom’s mass, making the nucleus very dense.