The X-X bond energy in the hypothetical gas, X2 is 153 kJ/mol.

a. How much energy, in joules, is required to break the bond in a single X-X molecule?
b. What wavelength of electromagnetic radiation would have the energy required to
break the X-X bond?
c. In what region of the spectrum (X-ray, UV, Vis, IR, etc.) does this radiation appear?

a. 153 kJ/mol = 153 kJ/6.022E23 kJ/molcule and that divided by 2 is kJ/atom.

b. In a single molecule it will be
E = hc/wavelength.

c. After you work it out, compare with a set of tables (perhaps one is in your book) giving the wavelength of parts of the electromagnetic spectrum). My guess, but that's all it is, is to look between the x-ray and violet visible region.

a. To find the energy required to break the X-X bond in a single molecule, you need to convert the given value from kilojoules per mole (kJ/mol) to joules per molecule. One mole contains Avogadro's number (6.022 x 10^23) of molecules. So, to convert kJ/mol to J/molecule, divide the given value by Avogadro's number:

Energy per molecule = (Energy per mole) / Avogadro's number

Energy per molecule = 153 kJ/mol / 6.022 x 10^23 molecules/mol

b. To find the wavelength of electromagnetic radiation required to break the X-X bond, you can utilize the equation:

Energy = Planck's constant * speed of light / wavelength

We're given the energy required (in joules) from part (a). Rearranging the equation, we get:

Wavelength = Planck's constant * speed of light / Energy

Substitute the known values into the equation, where Planck's constant is 6.626 x 10^-34 J*s and the speed of light is 3.00 x 10^8 m/s.

c. Once you have the wavelength from part (b), you can determine the region of the electromagnetic spectrum where the radiation appears. Below are the general regions of the spectrum:

- X-rays have wavelengths from about 10 picometers (pm) to 10 nanometers (nm).
- Ultraviolet (UV) radiation ranges from about 10 nm to 400 nm.
- Visible light (Vis) spans from about 400 nm to 700 nm.
- Infrared (IR) radiation ranges from about 700 nm to 1 millimeter (mm).

Compare the calculated wavelength with the given regions of the spectrum to determine the specific range where the radiation appears.