Answer
The screen should be a distance of $~~4.85\times 10^{7}~m~~$ from the lamp.
Work Step by Step
In part (a), we found that photons are emitted at a rate of $~~2.96\times 10^{20}~photons/s$
We can find $r$ such that the surface area of a sphere is $2.96\times 10^{20}~cm^2$:
$4\pi~r^2 = 2.96\times 10^{20}~cm^2$
$r^2 = \frac{2.96\times 10^{20}~cm^2}{4\pi}$
$r = \sqrt{\frac{2.96\times 10^{20}~cm^2}{4\pi}}$
$r = 4.85\times 10^{7}~m$
The screen should be a distance of $~~4.85\times 10^{7}~m~~$ from the lamp.
