Which of the following wavelengths corresponds to the longest wavelength of radiation that has enough energy to break a carbon-carbon single bond (bond energy ≈ 348 kJ/mol)?

• A. 210 nm
• B. 344 nm
• C. 120 nm
• D. 500 nm

Answer: (B)

Verified step by step guidance

1. Understand that the problem asks for the longest wavelength of radiation that can break a carbon-carbon single bond, which means the radiation must have at least the bond dissociation energy (348 kJ/mol).
2. Recall the relationship between energy and wavelength of electromagnetic radiation: \(E = \frac{hc}{\lambda}\), where \(E\) is the energy of one photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.
3. Convert the bond energy from kJ/mol to energy per photon by dividing by Avogadro's number: \(E_{photon} = \frac{348 \times 10^3 \text{ J/mol}}{6.022 \times 10^{23} \text{ mol}^{-1}}\).
4. Rearrange the equation to solve for the wavelength: \(\lambda = \frac{hc}{E_{photon}}\).
5. Calculate \(\lambda\) using the constants \(h = 6.626 \times 10^{-34} \text{ J}\cdot\text{s}\) and \(c = 3.00 \times 10^8 \text{ m/s}\), then compare the calculated wavelength to the given options to identify the longest wavelength that has enough energy to break the bond.