Answer
a. 2.12 eV
b. $1.35\times10^{15} photons/mm^2 $.
Work Step by Step
a. Find the photon energy.
$$E=hf=h\frac{c}{\lambda}$$
$$E=\frac{1.24\times10^{-6}eV\cdot m}{585\times10^{-9}m }= 2.12eV$$
b. We know the power of the laser beam is 20.0W, and the pulse is 0.45 ms long, so (20W)(0.00045s)=0.009J per pulse is delivered. This is $5.63\times10^{16}$ eV. The number of photons delivered per pulse can then be calculated.
$$N=\frac{5.63\times10^{16}eV/pulse}{2.12eV /photon}=2.65\times10^{16} photons/pulse$$
Finally, calculate the photons per square mm as follows:
$$\frac{2.65\times10^{16} photons}{\pi (2.5mm)^2}=1.35\times10^{15} photons/mm^2 $$
