Final answer:
The wavelength of radiation with an energy content of 3.55 × 10^3 kJ/mol is 9.29 nm.
Step-by-step explanation:
The wavelength (λ) of radiation can be calculated using the equation: c = λν, where c is the speed of light (3.00 × 10^8 m/s) and ν is the frequency of the radiation. To find the wavelength of radiation with an energy content of 3.55 × 10^3 kJ/mol, we need to convert the energy into joules per photon using the equation: 1 kJ/mol = 6.022 × 10^23 J/photon. Once we have the energy per photon, we can use the equation E = hν, where E is the energy and h is Planck's constant (6.626 × 10^-34 J·s), to find the frequency. Then, we can rearrange the equation c = λν to solve for the wavelength (λ).
Step-by-step explanation:
- Convert the energy into joules per photon: 3.55 × 10^3 kJ/mol × (6.022 × 10^23 J/photon / 1 kJ/mol) = 2.14 × 10^-20 J/photon.
- Use the equation E = hν to find the frequency: 2.14 × 10^-20 J/photon = (6.626 × 10^-34 J·s)ν. Solve for ν: ν = (2.14 × 10^-20 J/photon) / (6.626 × 10^-34 J·s) = 3.23 × 10^13 Hz.
- Use the equation c = λν to find the wavelength: (3.00 × 10^8 m/s) = λ × (3.23 × 10^13 Hz). Solve for λ: λ = (3.00 × 10^8 m/s) / (3.23 × 10^13 Hz) = 9.29 × 10^-6 m = 9.29 nm.