Answer
See explanation.
Work Step by Step
a. 193 nm is in the ultraviolet region.
b. Find the photon energy.
$$E=hf=h\frac{c}{\lambda}$$
$$E=\frac{1.24\times10^{-6}eV\cdot m}{193\times10^{-9}m }= 6.42eV$$
c. We know the power of the laser beam is 1.50mW, and the pulse is 12.0 ns long, so $(1.50\times10^{-3}W)(12.0\times10^{-9}s)=1.80\times10^{-11}J$ per pulse is delivered. This is $1.13\times10^{8}$ eV. The number of photons delivered per pulse can then be calculated.
$$N=\frac{1.13\times10^{8}eV/pulse}{6.42eV /photon}=1.75\times10^{7} photons/pulse$$
