For a rectangular metal surface with dimensions $5$ cm by $3$ cm$,$ the threshold wavelength for the

photoelectric emission of electrons is $246\mathrm{.}0$ nm$.$

$($a$)$ Calculate the work function of the metal surface.

$($b$)$ Calculate the wavelength of light that must be used in order for electrons with a maximum

kinetic energy of $2\mathrm{.}3$ eV to be ejected.

$($c$)$ If light of wavelength $300$ nm and intensity $1\mathrm{.}75$ W$/$m$2$ is incident normally on the metal

surface, calculate the number of photons that strike the surface in a time of $30$ seconds.

$7.($B$)$ After colliding with a free electron an x$-$ray photon is scattered through an angle of $700.$ The

wavelength of