30.1

Rutherford Scattering and the Nuclear Atom

An atom contains a small, positively charged nucleus , which is surrounded at relatively large distances by a number of electrons, as Figure 30-1 illustrates. In the natural state, an atom is electrically neutral because the nucleus contains a number of protons (each with a charge of + e) that equals the number of electrons (each with a charge of −e). This model of the atom is universally accepted now and is referred to as the nuclear atom.

Figure 30-1 In the nuclear atom a small positively charged nucleus is surrounded at relatively large distances by a number of electrons.

The nuclear atom is a relatively recent idea. In the early part of the twentieth century a widely accepted model, due to the English physicist Joseph J. Thomson (1856–1940), pictured the atom very differently. In Thomson’s view there was no nucleus at the center of an atom. Instead, the positive charge was assumed to be spread throughout the atom, forming a kind of paste or pudding, in which the negative electrons were suspended like plums.
The “plum-pudding” model was discredited in 1911 when the New Zealand physicist Ernest Rutherford (1871–1937) published experimental results that the model could not explain. As Figure 30-2 indicates, Rutherford and his co-workers directed a beam of alpha particles ( particles) at a thin metal foil made of gold. Alpha particles are positively charged particles (the nuclei of helium atoms, although this was not recognized at the time) emitted by some radioactive materials. If the plum-pudding model were correct, the particles would be expected to pass nearly straight through the foil. After all, there is nothing in this model to deflect the relatively massive particles, since the electrons have a comparatively small mass and the positive charge is spread out in a “diluted” pudding. Using a zinc sulfide screen, which flashed briefly when struck by an particle, Rutherford and co-workers were able to determine that not all the particles passed straight through the foil. Instead, some were deflected at large angles, even backward. Rutherford himself said, “It was almost as incredible as if you had fired a fifteen-inch shell at a piece of tissue and it came back and hit you.” Rutherford concluded that the positive charge, instead of being distributed thinly and uniformly throughout the atom, was concentrated in a small region called the nucleus.

Figure 30-2 A Rutherford scattering experiment in which particles are scattered by a thin gold foil. The entire apparatus is located within a vacuum chamber (not shown).

But how could the electrons in a nuclear atom remain separated from the positively charged nucleus? If the electrons were stationary, they would be pulled inward by the attractive electric force of the nuclear charge. Therefore, the electrons must be moving around the nucleus in some fashion, like planets revolving around the sun. In fact, the nuclear model of the atom is sometimes referred to as the “planetary” model. The dimensions of the atom, however, are such that it contains a larger fraction of empty space than our solar system does, as Conceptual Example 1 discusses.

| Conceptual Example 1 | | | Atoms Are Mostly Empty Space

In the planetary model of the atom, the nucleus is analogous to the sun . Electrons orbit the nucleus like the earth orbits the sun. If the dimensions of the solar system had the same proportions as those of the atom, would the earth be closer to or farther away from the sun than it actually is?
Reasoning and Solution The radius of an electron orbit is one hundred thousand times larger than the radius of the nucleus: . If the radius of the earth’s orbit were one hundred thousand times larger than the radius of the sun, the earth’s orbit would have a radius of . This is more than four hundred times greater than the actual orbital radius of , so the earth would be much farther away from the sun. In fact, it would be more than ten times farther from the sun than Pluto is, which is our most distant planet and has an orbital radius of about . An atom, then, contains a much greater fraction of empty space than does our solar system.
Related Homework: Problem 4

Although the planetary model of the atom is easy to visualize, it too is fraught with difficulties. For instance, an electron moving on a curved path has a centripetal acceleration, as Section 5.2 discusses. And when an electron is accelerating, it radiates electromagnetic waves, as Section 24.1 discusses. These waves carry away energy. With their energy constantly being depleted, the electrons would spiral inward and eventually collapse into the nucleus. Since matter is stable, such a collapse does not occur. Thus, the planetary model, although providing a more realistic picture of the atom than the “plum-pudding” model, must be telling only part of the story. The full story of atomic structure is fascinating, and the next section describes another aspect of it.

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