An owl has good night vision because its eyes can detect a light intensity as small as 5.0*10^-13W/M^2. What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of 8.5nn and the light has a wavelength of 510nm?
Can anyone please give me some ideas to do it? THANKS A LOT!
To calculate the minimum number of photons per second that an owl eye can detect, we can use the concept of photon flux.
First, we need to calculate the total power incident on the owl's eye. The power incident on the eye can be calculated using the formula:
Power = Intensity × Area
The intensity of light is given as 5.0 × 10^-13 W/m^2, and the area can be calculated using the formula for the area of a circular pupil:
Area = π × (radius)^2
The radius of the pupil can be calculated using the diameter of 8.5 nm:
Radius = diameter/2 = 8.5 nm / 2
Once we have the power incident on the eye, we can calculate the number of photons per second using the formula:
Number of photons = Power / Energy per photon
The energy per photon can be calculated using the formula:
Energy per photon = Planck's constant × (speed of light / wavelength)
Let's calculate step by step:
1. Convert the diameter of the pupil from nm (nanometers) to meters:
diameter = 8.5 nm = 8.5 × 10^-9 m
2. Calculate the radius of the pupil:
radius = diameter/2 = 8.5 × 10^-9 m / 2
3. Calculate the area of the pupil:
Area = π × (radius)^2 = π × (8.5 × 10^-9 m / 2)^2
4. Calculate the power incident on the owl's eye:
Power = Intensity × Area = 5.0 × 10^-13 W/m^2 × Area
5. Calculate the energy per photon:
Energy per photon = Planck's constant × (speed of light / wavelength)
Planck's constant = 6.626 × 10^-34 J·s
Speed of light = 3.0 × 10^8 m/s
wavelength = 510 nm = 510 × 10^-9 m
6. Calculate the number of photons per second:
Number of photons = Power / Energy per photon
By following these steps, we can determine the minimum number of photons per second that an owl eye can detect.
To find the minimum number of photons per second that an owl's eye can detect, we need to use the formula that relates energy of a photon to the wavelength and intensity of light. The formula is:
Energy of a Photon (E) = (Planck's Constant (h) * Speed of Light (c)) / Wavelength (λ)
To calculate the energy of a photon, we first need to determine the intensity of light incident on the owl's eye.
Intensity (I) = Power (P) / Area (A)
In this case, the power is the energy of a single photon, and the area is the pupil's area.
Area of the Pupil (A) = π * (Radius of Pupil)^2
To find the radius of the pupil, we need to divide its diameter by 2.
Once we have the intensity, we can calculate the number of photons per second using the relationship:
Number of Photons (N) = Intensity (I) / Energy of a Photon (E)
Let's calculate step by step:
Step 1: Calculate the area of the pupil
Given:
Diameter of Pupil (d) = 8.5 nm
Radius of Pupil (r) = d / 2 = 8.5 nm / 2 = 4.25 nm = 4.25 * 10^-9 m
Area of Pupil (A) = π * (4.25 * 10^-9 m)^2
Step 2: Calculate the energy of a photon
Given:
Wavelength of light (λ) = 510 nm = 510 * 10^-9 m
Energy of a Photon (E) = (Planck's Constant (h) * Speed of Light (c)) / Wavelength (λ)
Step 3: Calculate the intensity of light
Given:
Intensity (I) = Energy of a Photon (E)
Step 4: Calculate the number of photons per second
Number of Photons (N) = Intensity (I) / Energy of a Photon (E)
By following these steps, we can find the minimum number of photons per second that an owl's eye can detect.
The energy into the owl eye is given, multiply that by the area of the eye.
Now the will be the energy per second.
To find the number of photons, planck's equation
Energy above*numberPhotos=hc/lambda
solve for the number of photons.