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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.

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Edufirst

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
whitneytr12

The minimum number of photons of green light, with 2.35x10⁻¹⁸ J of energy and 510 nm of wavelength, that can be detected by the human eye is 6.04 photons.    

The energy of a single photon is given by:

[tex] E_{1} = h\frac{c}{\lambda} [/tex]

Where:  

h: is the Planck constant = 6.62x10⁻³⁴ J*s

λ: is the wavelength of the green light = 510 nm = 510x10⁻⁹ m

c: is the speed of light = 3.00x10⁸ m/s

So, the energy of one photon is:    

[tex]E_{1} = h\frac{c}{\lambda} = 6.62 \cdot 10^{-34} Js\frac{3.00 \cdot 10^{8} m/s}{510 \cdot 10^{-9} m} = 3.89 \cdot 10^{-19} J[/tex]  

Now, since the energy of the green light detected by the human eye is 2.35x10⁻¹⁸ J, the minimum number of photons (n) to produce that amount of energy is:  

[tex] E_{n} = nE_{1} [/tex]

[tex] n = \frac{E_{n}}{E_{1}} = \frac{2.35 \cdot 10^{-18} J}{3.89 \cdot 10^{-19} J} = 6.04 [/tex]  

Therefore, the minimum number of photons of green light is 6.04 photons.

You can find more about energy here:

  • https://brainly.com/question/2250305?referrer=searchResults
  • https://brainly.com/question/6576580?referrer=searchResults

I hope it helps you!    

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