A $150$ V battery is connected across two parallel metal plates of area $28\mathrm{.}5$ cm$2$ and separation $8\mathrm{.}20$ m$.$ A beam of alpha particles $($charge $+2$e$+2$e$,$ mass $6\mathrm{.}64\backslash$times $10^27$kg$)$ is accelerated from rest through a potential difference of $1\mathrm{.}75$ kV and enters the region between the plates perpendicular to the electric field, as shown in $($Figure $1$