bei48482_FM

dfnt

2

cot csc^2 d (4.32)

The minus sign expresses the fact that fdecreases with increasing .

As we saw in Fig. 4.2, Geiger and Marsden placed a fluorescent screen a distance

rfrom the foil and the scattered alpha particles were detected by means of the scintil-

lations they caused. Those alpha particles scattered between and dreached a

zone of a sphere of radius rwhose width is rd. The zone radius itself is rsin , and

so the area dSof the screen struck by these particles is

dS(2rsin)(rd) 2 r^2 sind

 4 r^2 sin cos d

If a total of Nialpha particles strike the foil during the course of the experiment, the

number scattered into dat is Nidf. The number N() per unit area striking the screen

at , which is the quantity actually measured, is

N()

N() (4.1)

Equation (4.1) is the Rutherford scattering formula. Figure 4.4 shows how N() varies

with .

NintZ^2 e^4



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

Rutherford

scattering formula

Nint

4 

Z



e

0

2

KE



2

cot

2



csc^2 

2



d



4 r^2 sin

2



cos

2



d

Ni|df|



dS





2





2





2





2

Ze^2



4  0 KE

Rutherford Scattering 157

4.1 The Nuclear Atom

1. The great majority of alpha particles pass through gases and
   thin metal foils with no deflections. To what conclusion about
   atomic structure does this observation lead?


2. The electric field intensity at a distance rfrom the center of a
   uniformly charged sphere of radius Rand total charge Qis
   Qr 4  0 R^3 when r R. Such a sphere corresponds to the
   Thomson model of the atom. Show that an electron in this
   sphere executes simple harmonic motion about its center and
   derive a formula for the frequency of this motion. Evaluate the

frequency of the electron oscillations for the case of the hydro-

gen atom and compare it with the frequencies of the spectral

lines of hydrogen.

3. Determine the distance of closest approach of 1.00-MeV pro-
   tons incident on gold nuclei.

4.2 Electron Orbits

4. Find the frequency of revolution of the electron in the classical
   model of the hydrogen atom. In what region of the spectrum
   are electromagnetic waves of this frequency?

EXERCISES

It isn’t that they can’t see the solution. It is that they can’t see the problem. —Gilbert Chesterton

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