the retina of a human eye can detect light when radiant energy incident on it is at least 4.0x10^-17 J. For light that is 565 nm wavelength, how many phontons does this energy correspond to?
To determine the number of photons corresponding to an energy value, we need to use the relationship between energy (E) and the frequency (ν) or wavelength (λ) of light. The energy of a photon (E) is given by the equation E = hν, where h is Planck's constant (6.626 x 10^-34 J*s).
First, we need to find the frequency (ν) of the light using the relationship c = λν, where c is the speed of light (3.00 x 10^8 m/s). Rearranging the equation, we have ν = c/λ.
Given that the light has a wavelength (λ) of 565 nm (which can be converted to meters by dividing by 1,000,000,000), we can calculate the frequency (ν) as follows:
ν = (3.00 x 10^8 m/s) / (565 x 10^-9 m) = 5.31 x 10^14 Hz.
Now, we can calculate the energy per photon (E) using the equation E = hν:
E = (6.626 x 10^-34 J*s) * (5.31 x 10^14 Hz) = 3.51 x 10^-19 J.
Finally, to find the number of photons corresponding to the given energy (4.0 x 10^-17 J), we divide the energy by the energy per photon:
Number of photons = (4.0 x 10^-17 J) / (3.51 x 10^-19 J) ≈ 114.24 x 10^2, or approximately 1.14 x 10^4 photons.
Therefore, the energy of 4.0 x 10^-17 J corresponds to approximately 1.14 x 10^4 photons at a wavelength of 565 nm.