A narrow beam of protons with velocity `v=6.10^(6)m//s` falls normally on a silver foil of thickness `d= 1.0 mu m`. Find the probability of the protons to be scattered into the rear hemisphere `(theta gt 90^(@))`.

Explanation

The requisite probability can be written easily by analogy with (b) of the presious problem.
It is
`P=(N(pi//2))/(I_(0)tau)=nd((Ze^(2))/((4piepsilon_(0))2mv^(2)))^(2)4piint_(pi//2)^(x)(cos theta//2d theta)/("sin"^(3)(theta)/(2))`
The intergal is unity. Thus
`P= pind((Ze^(2))/((4pi epsilon_(0))mv^(2)))^(2)`
Substitution gives using
`n=(rho_(Ag)N_(A))/(A_(Ag))=(10.5xx10^(3)xx6.023xx10^(26))/(108),P= .006`