Final answer:
The total energy contained in 1 mole of 645 nm photons is approximately 1.84 x 10⁵ J/mole.
Step-by-step explanation:
The question asks about the total energy contained in 1 mole of 645 nm photons. To find the energy of one photon, we can use the formula E = hc/λ, where E is the energy, 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 of the photon.
For a wavelength of 645 nm (which is 645 x 10⁻⁹ m), the energy of one photon is:
E = (6.626 x 10⁻³⁴ J·s)(3.00 x 10⁸ m/s) / (645 x 10⁻⁹ m)
= 3.06 x 10-19 joules per photon.
Since 1 mole of photons contains Avogadro's number of photons (approximately 6.022 x 10²³ photons/mole), the total energy for 1 mole of 645 nm photons is:
E(total) = 3.06 x 10⁻¹⁹ J/photon x 6.022 x 10²³ photons/mole
= 1.84 x 10⁵ J/mole.