Respuesta :
Explanation:
The given data is as follows.
  wavelength ([tex]\lambda[/tex]) = 415 nm
                    = [tex]415 \times 10^{-9} m[/tex] ( 1 nm = [tex]10^{-9}[/tex]m[/tex])
Relation between energy and wavelength is as follows.
      Energy (E) = [tex]\frac{hc}{\lambda}[/tex]
where, h = planck's constant = [tex]6.626 \times 10^{-34} J.s[/tex]
      c = velocity of light = [tex]3 \times 10^{8} m/s[/tex]
Therefore, calculate the energy as follows.
       Energy (E) = [tex]\frac{hc}{\lambda}[/tex]
                =  [tex]\frac{6.626 \times 10^{-34} J.s \times 3 \times 10^{8} m/s}{415 \times 10^{-9} m}[/tex]
                = [tex]0.0478 \times 10^{-17}[/tex] J
Hence, energy is equal to [tex]0.0478 \times 10^{-17}[/tex] J
As the number of photons in laser beam of 6W = [tex]\frac{6 J/s}{0.0478 \times 10^{-17}[/tex] J
                 = [tex]125.52 \times 10^{17}[/tex] per second
It is given that, diameter of the pinhole = 1.70 mm
Diameter of the beam = 6.40 mm
The ratio of pinhole area to area of beam  is as follows.
          [tex]\frac{\frac{\pi d^{2}_{pin}}{4}}{\frac{\pi d^{2}_{beam}}{4}}[/tex]
          = [tex]\frac{(1.70)^{2}}{(6.40)^{2}}[/tex]
          = [tex]\frac{2.89}{40.96}[/tex]
          = 0.0705
Hence, calculate the no. of photons of light travelling through pin hole per second  are as follows.
          = [tex]0.0705 \times 125.52 \times 10^{17}[/tex]
          = [tex]8.849 \times 10^{17}[/tex]
Therefore, Â we can conclude that no. of photons of light travelling through pin hole per second are [tex]8.849 \times 10^{17}[/tex] photons/s.
