A sodium lamp emits light at the power $\backslash ($ P$=120\backslash$mathrm$\{$~W$\}\backslash )$ and at the wavelength $\backslash (\backslash$lambda$=589\backslash$mathrm$\{$~nm$\}\backslash ),$ and the emission is uniformly in all directions. $($a$)$ At what rate are photons emitted by the lamp? $($b$)$ At what distance from the lamp will a totally absorbing screen absorb photons at the rate of $1\mathrm{.}00$ photon $\backslash (/\backslash$mathrm$\{$cm$\}^\{2\}\backslash$mathrm$\{$~s$\}\backslash )?($c$)$ What is the rate per square meter at which photons are intercepted by a screen at a distance of $1\mathrm{.}80$ m from the lamp?