Question

The cone cells of the human eye are sensitive to three wavelength ranges, which the eye interprets as blue (419nm), green (531 nm), and red(558nm). if the optic nerve in the eye requires 2.0x10^-17j of energy to initiate the sight impulses to the brain, how many photons of blue light, green light, and red

Answer 1

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Answer 2

The number of photons of blue light required is 42 photons of blue light

The number of photons of green light required is 53 photons of green light

The number of photons of red light required is 56 photons of red light

The energy of one photon of light is calculated using the formula:

E = h * c / λ

where h, Planck's constant  = 6.63 * 10⁻³⁴ Js

speed of light c = 3 * 10⁸ m/s

λ = wavelength of light

wavelength of blue light = 419 nm = 4.19 * 10⁻⁷ m

wavelength of green light = 531 nm = 5.31 * 10⁻⁷ m

wavelength of red light = 558 nm = 5.58 * 10⁻⁷ m

Number of photons of light = Energy of light / Energy of one photon of light

Energy of light required by optic nerve = 2.0 * 10⁻¹⁷ J

Energy of one photon of blue light,

E = (6.63 * 10⁻³⁴ Js * 3 * 10⁸ m/s) / 4.19 * 10⁻⁷ m = 4.74 * 10⁻¹⁹ J

Number of photons of blue light = 2.0 * 10⁻¹⁷ J / 4.74 * 10⁻¹⁹ J

Number of photons of blue light = 42 photons of blue light

Energy of one photon of green light,

E = (6.63 * 10⁻³⁴ Js * 3 * 10⁸ m/s) / 5.31 * 10⁻⁷ m = 3.74 * 10⁻¹⁹ J

Number of photons of green light = 2.0 * 10⁻¹⁷ J / 3.74 * 10⁻¹⁹ J

Number of photons of green light = 53 photons of green light

Energy of one photon of red light,

E = (6.63 * 10⁻³⁴ Js * 3 * 10⁸ m/s) / 5.58 * 10⁻⁷ m = 3.56 * 10⁻¹⁹ J

Number of photons of red light = 2.0 * 10⁻¹⁷ J / 3.56 * 10⁻¹⁹ J

Number of photons of red light = 56 photons of red light

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