The retina of a human eye can detect light when radiant energy incident on it is at least 4.00 × 10−17 J. For light of 535−nm wavelength, how many photons does this energy correspond to?

The number of photons is obtained by Plank's equation to be 108 photons.

According to Plank's theory;

E = nhf

But f = c/λ

Hence;

E =nhc/λ

Where;

E = energy of photon = 4.00 × J

n = number of photons = ?

h = Plank's constant  = 6.6 × Js

c = speed of light = 3 × m/s

λ = wavelength = 535 × m

n = Eλ/hc

n = 4.00 × × 535 × /6.6 × × 3 ×

= 108 photons

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1080 photons

Explanation:

ΔE = hc/λ => Energy per photon

h = 6.63 x 10⁻³⁴ j·s

c = 3 x 10⁸ m/s

λ= 535 nm = 5.35 x 10⁻⁷ m

ΔE/photon = (6.63 x 10⁻³⁴ j·s)(c = 3 x 10⁸ m/s)/(5.35 x 10⁻⁷ m) = 3.71 x 10⁻¹⁹ j/photon

For #photons in 4.00 x 10⁻⁷ j =  (4.00 x 10⁻⁷ j) / (3.71 x 10⁻¹⁹ j/photon) = 1076 photons ≅ 1080 photons (3 sig. figs.)