Final answer:
The energy contained in 1 mol of γ-ray photons with a wavelength of 2.35×10¹⁵ nm is calculated using the equation E = (hc) ⁄ λ, followed by multiplying by Avogadro's number. The result is 50.9 kJ/mol, which does not match any of the provided answer choices.
Step-by-step explanation:
To calculate the energy contained in 1 mol of γ-ray photons with a wavelength of 2.35×10¹⁵ nm, we will use the Planck's equation which relates the energy (E) of a photon to its wavelength (λ) and Planck's constant (h). The equation is E = (hc) / λ, where h is Planck's constant (6.626 x 10⁻³⁴ J·s) and c is the speed of light in a vacuum (approximately 3.00 x 10⁸ m/s).
First, convert the wavelength from nanometers (nm) to meters (m) by multiplying with 10⁻¹ m/nm. Then, plug the values into the equation to find the energy of a single photon. To find the energy per mole, multiply the single photon energy by Avogadro's number (6.022 x 10²³ mol⁻¹).
Step-by-step calculation:
Convert the wavelength to meters: 2.35 x 10¹⁵ nm x 10⁻¹ m/nm = 2.35 x 10⁻¹¹ m.
Calculate the energy of one photon using Planck's equation: E = (6.626 x 10⁻³⁴ J·s x 3.00 x 10⁸ m/s) / (2.35 x 10⁻¹¹ m) = 8.46 x 10⁻ J.
Calculate the energy per mole: 8.46 x 10⁻ J x 6.022 x 10²³ mol⁻¹ = 5.09 x 10³⁴ J/mol = 50.9 kJ/mol.
None of the answer choices correspond to the calculated value of 50.9 kJ/mol, so the correct answer choice must be calculated using a different wavelength or not listed among the options provided.