Question

A swimmer enters a gloomier world (in one sense) on diving to greater depths. Given that the mean molar absorption coefficient of sea water in the visible region is 6.2 x 10-5- L moI-1 cm-1, calculate the depth at which a diver will experience (a) half the surface intensity of light, (b) one-tenth the surface intensity

Answer 1

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.

Step-by-step explanation:

(a) We know that Lambert-Beer's law is as follows.

`log_(10) = (I_(o))/(I_(t)) = \epsilon * c * l`

As it is given that,

`(I_(o))/(I_(t)) = 2`

and,
`\epsilon = 6.2 * 10^(-3)`

We know that molarity of sea water is 599 mM.

`log_(10)(2) = 6.2 * 10^(-5) * 599 * 10^(-3) * l`

l =
`(0.301)/(6.2 * 10^(-5) * 599 * 10^(-3))`

= 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) We are given that,

`(I)/(I_(o)) = 10`

`log_(10)(10) = 6.2 * 10^(-5) * 599 * 10^(-3) * l`

l =
`(1)/(6.2 * 10^(-5) * 599 * 10^(-3) * l)`

= 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.