For scattering by an 'inverse square field' (such as that produced by a charged nucleus in Rutherford's model) the relation between impact parameter b and the scattering angle ` theta ` is given by
`b (Ze^2 cot (theta/2))/(4 pi epsi_0 ((mv^2)/(2)))`
a. What is the scattering angle for b =0?
b. For a given impact parameter h, does the angle of deflection increase or decrease with increasing energy?
c .What is the impact parameter at which the scattering angle is `90^@` for Z = 79 and initial energy of 10 MeV?
d. Why is it that the mass of the nucleus does not enter the formula above but the charge does?
e. For a given energy of the projectile, does the scattering angle increase or decrease with decrease in impact parameter?

Explanation

a.For b = 0, we get cot ` theta /2` = 0. It means` theta /2 = 90^@ `or 0= `180^@ `
b. Increase in b means increase in cot.`theta /2` i.e., decrease in `theta `.
c. Using `b =(Ze^2 cot "" theta /2)/( 4pi epsi_0 E )`, we get b= `1.1 xx 10^(-14)` m
d. Scattering occurs because of field due to the charge on nucleus. If Z=0, then `theta `=0. As recoil of nucleous is not consider , do mass of nueleous unimportant but in case recoil is not ignored, then small change in the relation is required.
e. Decrease in b means decrease in cot `theta /2`i.e., increase in scattering angle `theta`.