Respuesta :
Answer: (a) The depth at which a diver will experience half the surface intensity of light is 0.81 m.
(b) The depth at which a diver will experience one-tenth the surface intensity is 2.69 m.
Explanation:
(a) Â We know that Lambert-Beer's law is as follows.
  [tex]log_{10} = \frac{I_{o}}{I_{t}} = \epsilon \times c \times l[/tex]
As it is given that,
      [tex]\frac{I_{o}}{I_{t}} = 2[/tex]        Â
and, Â [tex]\epsilon = 6.2 \times 10^{-3}[/tex]
We know that molarity of sea water is 599 mM.
  [tex]log_{10}(2) = 6.2 \times 10^{-5} \times 599 \times 10^{-3} \times l[/tex]
    l = [tex]\frac{0.301}{6.2 \times 10^{-5} \times 599 \times 10^{-3}}[/tex]
    = 81 cm
    = 0.81 m
Therefore, the depth at which a diver will experience half the surface intensity of light is 0.81 m.
(b) Â We are given that,
       [tex]\frac{I}{I_{o}} = 10[/tex]
  [tex]log_{10}(10) = 6.2 \times 10^{-5} \times 599 \times 10^{-3} \times l[/tex]
        l = [tex]\frac{1}{6.2 \times 10^{-5} \times 599 \times 10^{-3} \times l}[/tex]
         = 269 cm
or,        = 2.69 m    (as 1 m = 100 cm)
Therefore, the depth at which a diver will experience one-tenth the surface intensity is 2.69 m.
