bei48482_FM

explain the results, Rutherford found, was to picture an atom as being composed of a

tiny nucleus in which its positive charge and nearly all its mass are concentrated, with

the electrons some distance away (Fig. 4.3). With an atom being largely empty space,

it is easy to see why most alpha particles go right through a thin foil. However, when

an alpha particle happens to come near a nucleus, the intense electric field there scat-

ters it through a large angle. The atomic electrons, being so light, do not appreciably

affect the alpha particles.

The experiments of Geiger and Marsden and later work of a similar kind also

supplied information about the nuclei of the atoms that composed the various tar-

get foils. The deflection of an alpha particle when it passes near a nucleus depends

on the magnitude of the nuclear charge. Comparing the relative scattering of alpha

particles by different foils thus provides a way to find the nuclear charges of the

atoms involved.

All the atoms of any one element turned out to have the same unique nuclear charge,

and this charge increased regularly from element to element in the periodic table. The

nuclear charges always turned out to be multiples of e; the number Zof unit

positive charges in the nuclei of an element is today called the atomic number of the

element. We know now that protons, each with a charge e, provide the charge on a

nucleus, so the atomic number of an element is the same as the number of protons in

the nuclei of its atoms.

Ordinary matter, then, is mostly empty space. The solid wood of a table, the steel

that supports a bridge, the hard rock underfoot, all are simply collections of tiny charged

particles comparatively farther away from one another than the sun is from the

planets. If all the actual matter, electrons and nuclei, in our bodies could somehow be

packed closely together, we would shrivel to specks just visible with a microscope.

Rutherford Scattering Formula

The formula that Rutherford obtained for alpha particle scattering by a thin foil on the

basis of the nuclear model of the atom is

N() (4.1)

This formula is derived in the Appendix to this chapter. The symbols in Eq. (4.1) have

the following meanings:

N() number of alpha particles per unit area that reach the screen at a

scattering angle of 

Nitotal number of alpha particles that reach the screen

n number of atoms per unit volume in the foil

Zatomic number of the foil atoms

rdistance of the screen from the foil

KE kinetic energy of the alpha particles

tfoil thickness

The predictions of Eq. (4.1) agreed with the measurements of Geiger and Marsden,

which supported the hypothesis of the nuclear atom. This is why Rutherford is credited

NintZ^2 e^4



(8 0 )^2 r^2 KE^2 sin^4 (2)

Rutherford

scattering formula

122 Chapter Four

Figure 4.3The Rutherford model

of the atom.

Electron Positive nucleus

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