6833.
Given Data :
The intensity of the energy at the human eye,
E1 = I*At
= I (4πr^2)t
After substituting the given value, we get :
E1 = ( 1.6 x 10-11 W/m^2 ) ( 4π ) ( 7* 10^-3 / 2 )^2 ( 1 s )
On solving the above eq., we get,
E1 = 2.46 x 10^-15 J
Photon energy at the human eye,
E2 = 12400 / 5500 eV
On solving the above eq., we get,
= 2.25 eV
= 2.25 eV x ( 1.6 x 10^-19 j / 1eV )
E2 = 3.6 x 10^-19 J
The number of photons entering the eye per second from the star,
N = E1 / E2
On solving the above eq., we get,
= 2.46 x 10^-15 j / 3.6 x 10^-19 j
N = 6833
And therefore, the number of photons entering the eye from the star per second are 6833.
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➤ Although your question isn't complete, I may have assumed that you were referring to this specific question.
The complete question is :
The human eye can barely detect a star whose intensity at the earth’s surface is 1.6 x 10-11 W/m2. If the dark-adapted eye has a pupil diameter of 7.0 mm, how many photons per second enter the eye from the star? Assume the starlight has a wavelength of 550 nm.
