Question

What is the longest wavelength of radiation with enough energy to break carbon-carbon bonds?

Answer 1

The longest wavelength of radiation used to break carbon-carbon bonds is 344 nm.

Explanation:

The longest wavelength of radiation can also be stated as the minimum radiation frequency required to cut carbon-carbon bond should be equal to the threshold energy of the carbon-carbon bonds.

The threshold energy will be equal to the binding energy of the carbon-carbon bonds. As it is known that carbon-carbon bonds exhibit a binding energy of 348 kJ/mole, the threshold energy to break it, is determined as followed.

First, we have to convert the energy from kJ/mol to J, i.e., energy for the carbon-carbon molecules,

$\text { Energy } = \frac{348 \mathrm{KJ} / \mathrm{mol}}{6.023 \times 10^{23} \text { photons }} \times 1 \text { mole } \times 1000 = 57.77 \times 10^{-20} = 5.78 \times 10^{-19} J$

As,

         $E=h v=\frac{h c}{\lambda}$

So,

$\lambda=\frac{h c}{E}=\frac{6.626 \times 10^{-34} \times 3 * 10^{8}}{5.78 \times 10^{-19}}=3.44 \times 10^{-7}$

Thus, $\lambda=344 \mathrm{nm}$ is the longest wavelength of radiation used to break carbon-carbon bonds.