Final answer:
The energy of radiation with a frequency of 4.00 × 10^14 s^-1 is calculated using Planck's equation and results in 159.6 kJ/mol after converting from joules to kilojoules per mole.
Step-by-step explanation:
To calculate the energy (E) of radiation using Planck's equation, which is E = hv, where h is Planck's constant and v is the frequency of the radiation, we first need to know the value of Planck's constant (h) and the given frequency (v). Planck's constant is 6.626 × 10^-34 J·s and the given frequency is 4.00 × 10^14 s^-1.
The energy E of a photon with frequency 4.00 × 10^14 s^-1 is:
E = (6.626 × 10^-34 J·s) × (4.00 × 10^14 s^-1) = 2.6504 × 10^-19 J.
To convert the energy to kilojoules per mole (kJ/mol), we use the fact that 1 mole of photons contains Avogadro's number of photons, which is approximately 6.022 × 10^23 photons/mol. Therefore, we multiply the energy of one photon by Avogadro's number:
E (kJ/mol) = (2.6504 × 10^-19 J/photon) × (6.022 × 10^23 photons/mol) × (1 kJ / 10^3 J) = 159.6 kJ/mol.