Answer
so an Owl can detect $291 photons $ per second.
Work Step by Step
An owl can detect light intensity
$I=5.0\times10^{-13}W/m^2=5.0\times10^{-13}J/(s.m^2)$
so it can detect $E=5.0\times10^{-13}J $ per second per square meter.
owl is having pupil of diameter $8.5mm=8.5\times10^{-3}m$
radius $r=\frac{8.5\times10^{-3}m}{2}=4.25\times10^{-3}m$
Area of pupil $=\pi r^2=3.14\times(8.5\times10^{-3}m)^2$
Area of pupil $=226.865\times10^{-6}m^2$$=2.26865\times10^{-4}m^2$
Energy detection by pupils per second $=intensity \times Area (pupil)$
Energy detection by pupils per second $=5.0\times10^{-13}J/(s.m^2) \times 2.26865\times10^{-4}m^2$
Energy detection by pupils per second $=11.34325\times10^{-17}J=1.134325\times10^{-16}J/s$
Energy detection by pupils per second is $E= 1.134325\times10^{-16}J/s$
(we have to concert this energy to number of photons)
Given that all photon are of wavelength $\lambda=510nm=510\times10^{-9}m=5.1\times10^{-7}m$
From Planks hypothesis
$E=\frac{hc}{\lambda}$
putting $h=6.63\times10^{-34}J.s$, $\lambda=5.1\times10^{-7}m$,, $c=3\times10^{8}m/s$
so Energy of one photon
$E=\frac{hc}{\lambda}=\frac{6.63\times10^{-34}J.s\times3\times10^{8}m/s}{5.1\times10^{-7}m}=3.9\times10^{-19}J$
Now since $3.9\times10^{-19}J$ is equal to $1$ photon
$1J$ will be equal to $\frac{1}{3.9\times10^{-19}}$photons
so $1.134325\times10^{-16}J$ is equal to $\frac{1.134325\times10^{-16}}{3.9\times10^{-19}}$photons=$0.29085\times10^{3}$ photons
or $0.29085\times10^{3}$ photons $=290.85\approx291$photons
so an Owl can detect 291photon per second.
