Photochromic Sunglasses Which Darken When Exposed To Light

Photochromic Sunglasses Which Darken When Exposed To Light Contain A

Photochromic sunglasses, which darken when exposed to light, contain a small amount of colorless AgCl embedded in the glass. When irradiated with light, metallic silver atoms are produced and the glass darkens: AgCl → Ag + Cl. Escape of the chlorine atoms is prevented by the rigid structure of the glass, and the reaction therefore reverses as soon as the light is removed. If 310 kJ/mol of energy is required to make the reaction proceed, what wavelength of light is necessary?

Paper For Above instruction

Photochromic sunglasses are a fascinating application of light-sensitive chemical reactions, specifically involving silver chloride (AgCl). These sunglasses contain embedded AgCl that undergoes a reversible photochemical transformation, darkening when exposed to light due to the formation of metallic silver. The core question addresses the energy requirement for this reaction and links it to the wavelength of light necessary to trigger the process.

Understanding the chemistry behind these sunglasses involves examining the reaction of silver chloride under illumination; the reaction can be summarized as:

AgCl (s) + energy → Ag (s) + Cl (g)

This process is photochemically initiated; photons provide the energy needed to reduce Ag+ ions to metallic silver atoms. The energy barrier for this process has been specified as 310 kJ/mol, indicating the minimum energy per mole required to initiate the reaction.

To determine the wavelength of light needed, one must relate the energy of individual photons to the energy per mole, which involves understanding the quantum nature of electromagnetic radiation. The energy (E) of a single photon is related to its wavelength (λ) by the equation:

E = hc/λ

where:

  • h = Planck’s constant (6.626 x 10-34 J·s)
  • c = speed of light (3.00 x 108 m/s)

Since the energy given is per mole, we need to convert the molar energy into energy per photon. Avogadro’s number (NA) = 6.022 x 1023 mol-1 allows us to find the energy of a single photon:

Ephoton = (310,000 J/mol) / (6.022 x 1023 mol-1) ≈ 5.15 x 10-19 J

Next, rearranging the photon energy equation to solve for wavelength:

λ = hc / Ephoton

Substituting known values:

  • h = 6.626 x 10-34 J·s
  • c = 3.00 x 108 m/s
  • Ephoton ≈ 5.15 x 10-19 J

Calculating λ:

λ = (6.626 x 10-34 J·s × 3.00 x 108 m/s) / 5.15 x 10-19 J ≈ 3.86 x 10-7 m

Expressed in nanometers, this wavelength is approximately:

λ ≈ 386 nm

This wavelength falls within the ultraviolet (UV) region of the electromagnetic spectrum but very close to the visible range, indicating that light with wavelengths around 386 nm supplies enough energy to initiate the darkening process in the photochromic sunglasses.

In summary, the energy required to initiate the reaction correlates directly with the photon wavelength. The calculations demonstrate that light with a wavelength near 386 nanometers — just on the edge of violet light — is necessary to activate the silver chloride in the sunglasses. This understanding is integral to designing and optimizing photochromic materials, ensuring they respond efficiently to sunlight or artificial light sources within specific spectral regions (Zhao et al., 2021; Bai et al., 2018). Achieving a balance between energy requirements and visual comfort requires precise control over the chemical composition and spectral responsiveness of these innovative eyewear products.

References

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