Question

A swimmer enters a gloomier world (in one sense) on diving to greater depths. Given that the mean molar absorption coeffi cient of seawater in the visible region is 6.2 × 10−5 dm3 mol−1 cm−1 , calculate the depth at which a diver will experience (a) half the surface intensity of light and (b) one-tenth that intensity.

Answer 1

a) x= 1,118 10⁴ m, b) x= 3.7 104 m

Step-by-step explanation:

To calculate the decrease in intensity with depth, write the equation

I = I₀
`e^(- \alpha x)`

Where Io is the intensity at the surface and alf is the absorption coefficient

Ln (I / I₀) = - α x

x = -1 /α ln (I / I₀)

Let's apply this expression to our case

a) intensity is half of the surface

I / I₀ = 0.5

We calculate

x = -1 /6.2 10⁻⁵ ln (0.5)

x = 0.1118 10⁵ m = 1,118 10⁴ m

b) the intensity is one tenth

I / Io = 0.1

x = -1 / 6.2 10⁵ ln (0.1)

x = 0.37138 10⁵ = 3.7 104 m