A small shot of negligible radius hits a stationary smooth, hard sphere of radius R, making an angle β with the normal to the sphere, as shown in Figure 4-25. It is reflected at an equal angle to the normal. The scattering angle is θ = 180º - 2β, as shown.

(a) Show by the geometry of the figure that the impact parameter b is related to θ by b = R cos1/2 θ.

(b) If the incoming intensity of the shot is I₀ particles/s . area, how many are scattered through angles greater than θ?

(c) Show that the cross section for scattering through angles greater than 0º is πR².

(d) Discuss the implication of the fact that the Rutherford cross section for scattering through angles greater than 0º is infinite.

Transcribed Image Text:

b B/ 8 FIGURE 4-25 Small particle scattered by a hard sphere of radius R.