Question

The human eye is able to detect as little as 2.35 × 10–18 j of green light of wavelength 510 nm. Calculate the minimum number of photons of green light that can be detected by the human eye. Physical constants can be found here.

Answer 1

Answer:

• The minimum number of photons that can be detected by the human eye is 6.03 × 10 ¹⁶ photons.

Explanation:

The energy of one photon of light is related to the wavelength by the equation:

• E = h×c/λ

Where, E is the energy of one photon, h is the Planck's constant, c is the speed of light, and λ is the wavelength of the light.

You are given with λ = 510 nm (nanometers), which you must convert to m (meters), to use SI units ⇒ λ = 510 × 10⁻⁹ m.

The physical constansts needed are:

• Planck's constant, h = 6.63 × 10⁻³⁴ J.s

• Speed of light, in vacuum, c = 3.0 × 10⁻⁸ m/s

Now you can substitute in the formula can compute for the value of E:

• E = 6.63×10⁻³⁴ J.s × 3.0 × 10⁻⁸ m/s / (510×10⁻⁹ m) = 0.039 × 10⁻³³ J

Since, that is the energy of one photon of green light, to calculate the number of photons that can be detected by the human eye, you need to divide the amounf of energy the human eye is able to detect, 2.35 × 10⁻¹⁸ J , by the energy of a photon:

• number of photons = 2.35×10 ⁻¹⁸J / 0.039 × 10⁻³³ J/ photon

• number of photons = 60.3 × 10¹⁵ photons = 6.03 × 10¹⁶photons