for scattering by an inverse square law 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)/(4pi in_0(1/2mv^2))`
(a) What is the scattering angle for b=0?
(b) for given impact parameter, b, does the angle of deflection increase or decrease with increase in energy?
(c) What is the impact parameter at which the scattering angle is `90^@` for Z=79 and initial energy=10MeV?
(d) Why is it that the mass of the nucleus does not enter the formula above, but its charge does?
(e) for a given energy of the projectile, does the scattering angle increase or decrease with decrease in impact parameter?

Answer

`1.14xx10^(-14)m`

Explanation

Here, `b=? theta=90^(@), Z=79`
`E=10MeV =10xx1.6xx10^(-13)J`
`b=(Ze^(2)cot theta//2)/(4piepsilon_(0)(KE))`
`=(9xx10^(9)xx79(1.6xx10^(-19))^(2)cot 90^(@)//2)/(10xx1.6xx10^(-13))`
`b=(9xx79xx2.56xx1xx10^(-16))/16=1.14xx10^(-14)m`