$3)$ A DRAM chip utilizes a $1$T$-1$C $($one transistor and one capacitor$)$ configuration. The capacitance of each DRAM cell is engineered to preserve the stored data for a minimum of $60$ nanoseconds $($ns$)$ prior to requiring refreshment. Post$-$refresh, the voltage across the capacitor is assumed to be $1$ V $,$ with a threshold voltage of $0\mathrm{.}5$ V to ensure the data within the capacitor is not lost, and the capacitance value is $100$ pF $.$

a$)$ Calculate the minimum amount of charge that the capacitor needs to retain.

b$)$ With a leakage current causing a $\backslash (10\backslash \%\backslash )$ charge loss from the capacitor in $60$ ns $,$ determine the amount of charge lost within $60$ ns and whether this meets the design specifications for the refresh period