# How many photons per second?

The human eye can barley 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.

Please show equations and answers

### 2 Answers

- knrLv 61 decade agoFavorite Answer
with the given intensity of radiation ,we can have

energy at the eye E1 = I x A x t = I x pi r^2 x t

= 1.6x10^-11x 3.14x (3.5x10^-3)^2 x 1

= 6.1544 x10^-16 J

now energy of photon E2 = 12400 / wavelngth(in angstrom) ev

= 12400 / 5500 = 2.25 ev = 2.25x1.6x10^-19 J

= 3.6 x 10^-19 J

then number of photons N = E1/E2 = 6.1544x10^-16 / 3.6x10^-19 = 1709 (nearly)

- Al PLv 71 decade ago
h = 6.6260681 * 10 ^ -34 m2 kg / s

c = 3 * 10 ^ 8 m/s

P = 1.6 * 10 ^ -11 W/m^2

w = 550 * 10 ^ -9 m

r = 0.007 / 2 m

A = pi * r ^ 2

The total energy arriving in one second is:

E = P * A * 1 = 6.1575164E-16 J

Energy of one photon

Ep = h * c / w

Photon_Number = E / Ep

Photon_Number = 1703.6921287704

With rounding:

Photon_Number = 1704 photons /s