The exposure unit in $SI$ system is defined as $1$ Coulomb $(C)$ of charge in one $kg$ of air. a$)$ If $1$ Roentgen $(R)$ of exposure is equivalent to production of $1$ esu $($electrostatic unit$)$ of one sign from the interaction of gamma radiation in $0\mathrm{.}001293$ gram of air, what is the exposure unit in Roentgen $(R).b$ If the exposure rate is $1m\frac{R}{sec}$ determine the ions being produced per $\frac{m^3}{sec}?1$ esu $=3\mathrm{.}33{10}^{-10}$Coulomb$\mathrm{.}18P$