bei48482_FM

with the “discovery” of the nucleus. Because N() is inversely proportional to sin^4 (2)

the variation of N() with is very pronounced (Fig. 4.4): only 0.14 percent of the

incident alpha particles are scattered by more than 1°.

Nuclear Dimensions

In his derivation of Eq. (4.1) Rutherford assumed that the size of a target nucleus is

small compared with the minimum distance Rto which incident alpha particles

approach the nucleus before being deflected away. Rutherford scattering therefore gives

us a way to find an upper limit to nuclear dimensions.

Let us see what the distance of closest approach Rwas for the most energetic alpha

particles employed in the early experiments. An alpha particle will have its smallest R

when it approaches a nucleus head on, which will be followed by a 180° scattering.

At the instant of closest approach the initial kinetic energy KE of the particle is entirely

converted to electric potential energy, and so at that instant

KEinitialPE

since the charge of the alpha particle is 2eand that of the nucleus is Ze. Hence

R (4.2)

2 Ze^2



4  0 KEinitial

Distance of closest

approach

2 Ze^2



R

1



4  0

Atomic Structure 123

Figure 4.4Rutherford scattering. N() is the number of alpha particles per unit area that reach the

screen at a scattering angle of ; N(180°) is this number for backward scattering. The experimental

findings follow this curve, which is based on the nuclear model of the atom.

N(θ)

N(180°)

0 ° 20 ° 40 ° 60 ° 80 ° 100 ° 120 ° 140 ° 160 ° 180 °

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