Question

Carbon-carbon bonds form the ""backbone"" of nearly every organic and biological molecule. The average bond energy of the C¬C bond is 347 kJ/mol. Calculate the frequency and wavelength of the least energetic photon that can break an average C¬C bond. In what region of the electromagnetic spectrum is this radiation?

Answer 1

1.17 × 10¹⁵ s⁻¹ is the frequency and the wavelength is 3.43 × 10⁻⁷m of the least energetic photon that can break an average C - C bond.

WHAT IS CARBON BACKBONE ?

The carbon backbone is also called the carbon skeleton. All organic compounds are made up of carbon-carbon bonds, creating a carbon skeleton or backbone in the compounds.

Carbon Skeleton Structure :

The carbon skeleton structures consist of bending lines, periodically other elements are written in as well. The carbon skeleton characteristics that change the overall structure includes:

• Length of carbon chain (the longer it is the more zig-zags are drawn).
• Shape of the carbon chain (branches, rings, etc. all change the shape of the skeleton).
• Location of attached functional groups, they need to be put onto the correct point in the skeleton.
• Any double or triple bonds that are present, particularly as triple bonds change the shape of the skeleton.

What is wavelength?

Forms of electromagnetic radiation like radio waves, light waves or infrared (heat) waves make characteristic patterns as they travel through space. Each wave has a certain shape and length. The distance between peaks (high points) is called wavelength.

Step 1 :

Here we have to calculate the frequency and wavelength of the least energetic photon that can break an average C - C bond and have to find out in what region of the electromagnetic spectrum is this radiation.

Bond energy of C - C = 347 kJ

It is known that E = hv

           ⇒ $mu = \frac{E}{h}$

Where, E is the energy = 347kJ

            h is the planck's constant = $6.626 * 10^{-34}J.s$

            v is the frequency

Now substituting the values, frequency can be calculated as,

             ⇒ $v = \frac{E}{h} = \frac{347kJ/1kJ * mol/6.022 * 10^{23}}{6.626 * 10^{-34}J.s}$

                             ≈ 8.70 × 10¹⁴ s⁻¹ .

Formula of Wavelength :

              $\lambda = \frac{hc}{E}$

Where, λ = wavelength

            h = 6.6 × 10⁻³⁴

            c = 3 × 10⁸

            E = bond energy

Now substituting the values, wavelength can be calculated as,

$\lambda = \frac{hc}{E} = \frac{6.6 * 10^{-34} * 3 * 10^{8} * 6.023 * 10^{23}}{347 * 10^{3}} = \frac{119.255 * 10^{-34} * 10^{31} * 10^{-3}}{347} = 0.343 * 10^{-6} = 3.43*10^{-7} m$

Thus, from the above conclusion we can say that 1.17 × 10¹⁵ s⁻¹ is the frequency and the wavelength is 3.43 × 10⁻⁷ m of the least energetic photon that can break an average C - C bond.

Learn more about the wavelength and frequency here :

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