bei48482_FM

124 Chapter Four

The maximum KE found in alpha particles of natural origin is 7.7 MeV, which is

1.2  10 ^12 J. Since 1 4  0 9.0 109 Nm^2 /C^2 ,

R

3.8 10 ^16 Z m

The atomic number of gold, a typical foil material, is Z79, so that

R(Au)3.0 10 ^14 m

The radius of the gold nucleus is therefore less than 3.0  10 ^14 m, well under

10 ^4 the radius of the atom as a whole.

In more recent years particles of much higher energies than 7.7 MeV have been

artificially accelerated, and it has been found that the Rutherford scattering formula

does indeed eventually fail to agree with experiment. These experiments and the in-

formation they provide on actual nuclear dimensions are discussed in Chap. 11.

The radius of the gold nucleus turns out to be about ^15 of the value of R(Au) found

above.

(2)(9.0 109 Nm^2 /C^2 )(1.6 10 ^19 C)^2 Z



1.2 10 ^12 J

4.2 ELECTRON ORBITS

The planetary model of the atom and why it fails

The Rutherford model of the atom, so convincingly confirmed by experiment, pictures

a tiny, massive, positively charged nucleus surrounded at a relatively great distance by

enough electrons to render the atom electrically neutral as a whole. The electrons can-

not be stationary in this model, because there is nothing that can keep them in place

against the electric force pulling them to the nucleus. If the electrons are in motion,

however, dynamically stable orbits like those of the planets around the sun are pos-

sible (Fig. 4.5).

Let us look at the classical dynamics of the hydrogen atom, whose single electron

makes it the simplest of all atoms. We assume a circular electron orbit for convenience,

though it might as reasonably be assumed to be elliptical in shape. The centripetal

force

Fc

m^2



r

Figure 4.5Force balance in the

hydrogen atom.

Electron

r

Proton+e F F v–e

Neutron Stars

T

he density of nuclear matter is about 2.4 1017 kg/m^3 , which is equivalent to 4 bil-

lion tons per cubic inch. As discussed in Sec. 9.11, neutron stars are stars whose atoms

have been so compressed that most of their protons and electrons have fused into neutrons,

which are the most stable form of matter under enormous pressures. The densities of neu-

tron stars are comparable to those of nuclei: a neutron star packs the mass of one or two

suns into a sphere only about 10 km in radius. If the earth were this dense, it would fit into

a large apartment house.

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