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it takes 463 kJ/mol to break an oxygen-hydrogen single bond. calculate the maximum wavelength of light for which an oxygen-hydrogen single bond could be broken by absorbing a single photon

Respuesta :

Edufirst

Answer:

  • 2.59 × 10⁻⁷ m  = 259 nm

Explanation:

You need to calculate the wavelength of a photon with an energy equal to 463 kJ/mol, which is the energy to break an oxygen-hydrogen atom.

The energy of a photon and its wavelength are related by the Planck - Einstein equation:

  • E = hν,

Where:

  • E = energy of a photon,
  • h = Planck constant (6.626 × 10⁻³⁴ J . s) and
  • ν = frequency of the photon.

And:

  • ν = c / λ

Where:

  • c = speed of light (3.00 × 10⁸ m/s in vacuum)
  • λ = wavelength of the photon

Thus, you can derive:

  • E = h c / λ

Solve for λ:

  • λ = h c / E

Before substituting the values, convert the energy, 463 kJ/ mol, to J/bond

  • 463 kJ/ mol × 1,000 J/kJ × 1 mol / 6.022 × 10 ²³ atom × 1 bond / atom

       = 7.69×10²³ J / bond

Substitute the values and use the energy of one bond:

  • λ = 6.626 × 10⁻³⁴ J . s × 3.00 × 10⁸ m/s / 7.69×10²³ J = 2.59 × 10⁻⁷ m

The wavelength of light is usually shown in nanometers:

  • 2.59 × 10⁻⁷ m × 10⁹ nm / m = 259 nm ← answer

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