At a spot in the ocean, the surface irradiance is 7.8*10^16 photons and k=.14 m^-1. At what depth does the euphotic zone end?
To determine the depth at which the euphotic zone ends, we need to use the equation known as the Beer-Lambert Law.
The Beer-Lambert Law describes the relationship between the absorption of light by a substance and the concentration of that substance, as well as the length of the path that the light travels through it. In this case, we will be using it to calculate the depth at which the light intensity decreases to a certain level.
The equation is given as:
I = I₀ * e^(-k * z)
Where:
I is the intensity of light at a depth z,
I₀ is the initial intensity of light at the surface,
k is the absorption coefficient of the water (provided in the question),
z is the depth.
Given that the surface irradiance (I₀) is 7.8 * 10^16 photons and k is 0.14 m^-1, we can rearrange the equation to solve for the depth z.
First, we need to determine the desired intensity level at which we consider the euphotic zone to end. Let's assume it decreases to 10% of the surface irradiance. Thus, I = 0.1 * I₀.
The equation becomes:
0.1 * I₀ = I₀ * e^(-k * z)
Simplifying, we have:
0.1 = e^(-k * z)
Now, take the natural logarithm (ln) of both sides:
ln(0.1) = -k * z
Rearranging to solve for z:
z = - ln(0.1) / k
Plug in the values:
z = - ln(0.1) / 0.14
Using a calculator, we find that z ≈ 0.693 / 0.14 ≈ 4.95 meters.
Therefore, the euphotic zone ends at a depth of approximately 4.95 meters.