Final answer:
To find the energy in kJ of one mole of x-rays with a 6.34 nm wavelength, use the energy-wavelength relationship for photons E = hc/λ, and multiply the energy of one photon by Avogadro's number, then convert from J to kJ.
Step-by-step explanation:
To calculate the energy in kilojoules (kJ) of one mole of x-rays with a wavelength of 6.34 nanometers (nm), we can use the energy-wavelength relationship for photons, which derives from Planck's equation: E = hc/λ, where E is the energy of a photon, h is Planck's constant (6.626 x 10-34 J·s), c is the speed of light (3.00 x 108 m/s), and λ is the wavelength in meters.
The energy for one mole of photons (Avogadro's number, 6.022 x 1023 photons per mole) can be calculated by multiplying the energy of a single photon by Avogadro's number. After obtaining energy in joules per mole (J/mol), convert the energy to kilojoules by dividing by 1,000 since 1 kJ = 1,000 J.
To find the energy in eV using the given relation in the prompt (E = 1.241 x 10-6 eV · m/λ), you would adjust the formula to account for moles, using 1 eV = 1.602 x 10-19 J for conversion.