$3.(20$ points$)$ In a Rutherford scattering experiment, a beam of Ek$=6\mathrm{.}0$ MeV particles

are scattered off a silver foil of $1\mathrm{.}0$m thickness. The beam current is $1\mathrm{.}0$ nA$.$

$($For silver, Z$=47,$ $=10\mathrm{.}5$ gm$/$cm$3,$ and molar mass M$=108$g$/$mol$)$

a$)(5$ points$)$ What fraction of particles are scattered backward $($i$.$e$.$ to angles of $90$

degrees or more$).$

b$)(10$ points$)$ How many particles per second will be counted by a small detector

of area $5\mathrm{.}0$ mm$2$ located $2$cm from the foil at an angle of $45$o$?$

c$)(5$ points$)$ If the above detector is moved to an angle of $75$o $($and still keep the

distance at $2$cm$),$ what is the count rate?