The energy from radiation can be used to rupture chemical bonds. A minimum energy of 192 kJ/mol is required to break the bromine–bromine bond in Br2. 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. First, we need to convert the energy required to break the bond from kJ/mol to Joules per photon. We know that 1 mol of photons contains Avogadro's number (6.022 x 10^23) of photons. So, divide 192 kJ/mol by Avogadro's number and convert kJ to J (1 kJ = 1000 J). This will give us the energy per photon in Joules.
2. Next, we use the energy of a photon equation, E = h*c/λ, where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J*s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength. We need to solve for λ, so rearrange the equation to λ = h*c/E.
3. Substitute the values of h, c, and E (the energy per photon in Joules we calculated in step 1) into the equation to find the wavelength in meters.
4. Convert the wavelength from meters to nanometers by multiplying by 1 x 10^9 (since 1 m = 1 x 10^9 nm). This will give us the wavelength in a more commonly used unit in this context.
5. Finally, to determine the type of electromagnetic radiation, refer to the electromagnetic spectrum. The type of radiation (radio, microwave, infrared, visible, ultraviolet, X-ray, or gamma ray) depends on the range of the wavelength.

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 longer wavelengths correspond to lower energy, while shorter wavelengths correspond to higher energy.

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 bromine–bromine bond in Br2 requires 192 kJ/mol to break, which indicates the strength of the bond and the energy needed from radiation to rupture it.

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 provide sufficient energy to break chemical bonds typically falls within the ultraviolet or higher energy regions of the spectrum, as these wavelengths have the necessary energy to exceed the bond dissociation energy.