The energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of 242 kJ/mol is required to break the chlorine–chlorine bond in Cl2. What is the longest wavelength of radiation that possesses the necessary energy to break the bond? What type of electromagnetic radiation is this?

Verified step by step guidance

1. Convert the energy required to break the bond from kJ/mol to J/molecule. Use the conversion factor: 1 kJ = 1000 J and Avogadro's number (6.022 x 10^23 molecules/mol).
2. Use the equation E = h\nu to relate energy (E) to frequency (\nu), where h is Planck's constant (6.626 x 10^-34 J·s). Rearrange the equation to solve for frequency: \nu = E/h.
3. Use the speed of light equation c = \lambda\nu, where c is the speed of light (3.00 x 10^8 m/s) and \lambda is the wavelength. Rearrange to solve for wavelength: \lambda = c/\nu.
4. Substitute the frequency calculated in step 2 into the equation from step 3 to find the wavelength.
5. Determine the type of electromagnetic radiation by comparing the calculated wavelength to the electromagnetic spectrum ranges.

Key Concepts

Energy and Wavelength Relationship

The energy of electromagnetic radiation is inversely related to its wavelength, described by the equation E = hc/λ, where E is energy, h is Planck's constant, c is the speed of light, and λ is the wavelength. This means that as the wavelength increases, the energy decreases. Understanding this relationship is crucial for determining the longest wavelength that can still provide sufficient energy to break a chemical bond.

Bond Dissociation Energy

Bond dissociation energy is the amount of energy required to break a specific chemical bond in a molecule, measured in kJ/mol. In this case, the chlorine–chlorine bond in Cl2 requires 242 kJ/mol to break. This concept is essential for calculating the energy needed from radiation to achieve bond rupture.

Types of Electromagnetic Radiation

Electromagnetic radiation encompasses a range of wavelengths and frequencies, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. The type of radiation that can break chemical bonds typically falls within the ultraviolet or higher energy regions, as these wavelengths possess sufficient energy to overcome bond dissociation energies.