We can calculate the energy of a single photon through Plank-Einstein relation. We have
[tex] E = hv[/tex]
where [tex]h[/tex] is the Plank's constant and [tex]v[/tex] is the frequency. Also, recall that to solve for the frequency, we have
[tex] v = \frac{c}{\lambda} [/tex]
where [tex]c[/tex] is the speed of light and [tex]\lambda[/tex] is the wavelength of the laser, in meters. So for this problem we can compute for [tex]v[/tex] with
[tex] v = \frac{3.10^{8} m/s}{683.10^{-9} m} \\ v = 4.39.10^{14}[/tex]
Going back to the Planck-Einstein relation, we have
[tex] E = (6.626.10^{-34} J.s)(4.39.10^14 s^{-1}) [/tex]
Hence, we have [tex] E = 2.91 x 10^{-19} J [/tex].
Given that the laser emits an energy of 0.258 J, then there are
[tex] number of photons = \frac{0.258}{2.91 x 10^{-19}} \\ number of photons = 7.5 x 10^{18} [/tex].
Answer: 7.5 ⋅ 10^18 photons
