An owl has good night vision because its eyes can detect a light intensity as small as 5.0*10^-13 W/m^2. What is the minimum number of photons per second that an owl eye can detect if its pupil has a diameter of 8.5mm and the light has a wavelength of 510nm?
I really got no idea how to do it!!!PLEASE GUIDE ME STEP BY STEP!THANKS A LOT!!
Sure! Let's break down the problem step by step:
Step 1: Calculate the area of the owl's pupil:
The formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius of the circle. In this case, the diameter of the pupil is given as 8.5mm, so the radius would be half of that, which is 4.25mm.
Converting the radius from mm to meters:
1mm = 0.001m
Therefore, 4.25mm = 4.25 * 0.001 = 0.00425m
Calculating the area:
A = π(0.00425)^2 = 0.056807 m^2
Step 2: Calculate the energy of one photon:
The energy of a photon can be calculated using the formula E = hc/λ, where E is the energy, h is Planck's constant (6.626 x 10^-34 Js), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of the light.
Substituting the given values:
E = (6.626 x 10^-34 Js)(3 x 10^8 m/s)/(510 x 10^-9 m)
E = (19.878 x 10^-26 Jm)/(510 x 10^-9 m)
E = (19.878/510) x 10^-17 J = 3.896 x 10^-20 J
Step 3: Calculate the power of one photon:
The power of one photon can be calculated using the formula P = E/t, where P is the power, E is the energy of the photon, and t is the time taken for the photon to be detected. In this case, we want to find the power of one photon per second.
P = (3.896 x 10^-20 J)/(1s) = 3.896 x 10^-20 W
Step 4: Calculate the minimum number of photons per second:
To find the minimum number of photons per second that an owl eye can detect, we need to divide the minimum intensity by the power of one photon.
Minimum intensity = 5.0 x 10^-13 W/m^2
Number of photons per second = Minimum intensity / Power of one photon
Number of photons per second = (5.0 x 10^-13 W/m^2) / (3.896 x 10^-20 W)
Number of photons per second ≈ 1.28415 x 10^7 photons
Therefore, the minimum number of photons per second that an owl eye can detect is approximately 1.28415 x 10^7 photons.
Sure! I'd be happy to guide you step by step.
To find the minimum number of photons per second that an owl eye can detect, we need to calculate the number of photons arriving at the owl's eye per second.
Step 1: Calculate the area of the owl's pupil.
The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. In this case, the owl's pupil has a diameter of 8.5mm, so the radius can be calculated as half of that value.
Radius (r) = diameter / 2 = 8.5mm / 2 = 4.25mm = 0.00425m
Now we can calculate the area of the owl's pupil:
Area (A) = π(0.00425)^2
Step 2: Calculate the power incident on the owl's eye.
The power incident on the owl's eye can be calculated using the formula P = I * A, where P is the power, I is the light intensity, and A is the area of the pupil.
Given that the light intensity is 5.0*10^-13 W/m^2 and we calculated the area of the pupil in Step 1, we can substitute these values into the equation:
Power (P) = (5.0*10^-13) * (Area)
Step 3: Calculate the energy of one photon.
The energy of one photon can be calculated using the formula E = hc / λ, where E is the energy of one photon, h is Planck's constant (6.63*10^-34 J*s), c is the speed of light (3.0*10^8 m/s), and λ (lambda) is the wavelength of the light.
Given that the wavelength of the light is 510nm, we can convert it to meters by dividing by 10^9:
Wavelength (λ) = 510nm / (10^9) = 5.1*10^-7 m
Now, we can substitute the values into the equation:
Energy of one photon (E) = (6.63*10^-34) * (3.0*10^8) / (5.1*10^-7)
Step 4: Calculate the minimum number of photons.
The minimum number of photons can be calculated by dividing the power incident on the owl's eye (calculated in Step 2) by the energy of one photon (calculated in Step 3). This will give us the number of photons per second.
Minimum number of photons = Power / Energy of one photon
Substituting the values:
Minimum number of photons = Power / (6.63*10^-34) * (3.0*10^8) / (5.1*10^-7)
Finally, perform the multiplication and division to get the minimum number of photons per second.