Question

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

Answer 1

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