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 need to consider the intensity of light and the energy of individual photons.
1. First, let's calculate the area of the owl's pupil:
- The formula for the area of a circle is A = π * r^2.
- The diameter of the pupil is given as 8.5 nm, so the radius (r) would be half of that, which is 4.25 nm.
- Convert the radius to meters by dividing by 10^9: 4.25 nm / 10^9 = 4.25 * 10^-9 meters.
- Now, calculate the area of the pupil: A = π * (4.25 * 10^-9)^2 square meters.
2. Next, let's calculate the power (P) incident on the pupil:
- The power density (I) is given as 5.0 * 10^-13 W/m^2.
- The power (P) incident on the pupil can be calculated using the formula P = I * A, where A is the area of the pupil that we calculated above.
3. Now, let's calculate the energy (E) of an individual photon:
- The wavelength (λ) of the light is given as 510 nm.
- The energy (E) of a photon can be calculated using the formula E = h * c / λ, where h is Planck's constant (6.626 * 10^-34 J·s) and c is the speed of light (3.0 * 10^8 m/s).
4. Finally, we can calculate the minimum number of photons (N) per second:
- Divide the power (P) incident on the pupil by the energy (E) of an individual photon to get the number of photons per second: N = P / E.
By following these steps, you should be able to calculate the minimum number of photons per second that an owl eye can detect.
Sure, I can help you with that! To calculate the minimum number of photons per second that an owl eye can detect, you can follow these steps:
1. Calculate the area of the owl's pupil:
Given the diameter of the pupil (8.5 nm), you can calculate the radius by dividing it by 2 (4.25 nm). Then, use the formula for the area of a circle, A = πr^2, to calculate the area of the pupil.
2. Calculate the power incident on the pupil:
You can use the formula for power, P = IA, where I is the intensity of light (5.0*10^-13 W/M^2) and A is the area of the pupil calculated in step 1.
3. Calculate the energy of a single photon:
The energy of a photon can be calculated using the equation E = hc/λ, where h is Planck's constant (approximately 6.62607015 × 10^-34 J·s), c is the speed of light in a vacuum (approximately 3.0 × 10^8 m/s), and λ is the wavelength of light (510 nm).
4. Calculate the number of photons per second:
Divide the power incident on the pupil (calculated in step 2) by the energy of a single photon (calculated in step 3) to find the minimum number of photons per second that an owl eye can detect.
I hope this helps! Let me know if you need further assistance with any of the steps.