Final answer:
To find the energy of 5 moles of photons with a wavelength of 582 nm, calculate the energy of one photon using Planck's constant and the speed of light, then multiply by Avogadro's number and the number of moles.
Step-by-step explanation:
To calculate the energy of 5 moles of photons with a given wavelength, you will need to use the energy equation for a single photon and then scale it up to the amount for moles of photons. The energy (E) of a single photon can be determined by the equation E = hc/λ, where h is Planck's constant (6.626 × 10-34 J·s), c is the speed of light (3.00 × 108 m/s), and λ is the wavelength in meters. To find the energy for 5 moles of photons, you'll multiply the energy of one photon by Avogadro's number (6.022 × 1023 photons/mol) and then by the number of moles (5).
First, convert wavelength from nanometers to meters: λ = 582 nm = 582 × 10-9 m. Now calculate the energy of a single photon: E = (6.626 × 10-34 J·s) (3.00 × 108 m/s) / (582 × 10-9 m). Then multiply this energy by Avogadro's number and by 5 moles to find the total energy.
Step-by-step calculation:
- Convert wavelength to meters: λ = 582 × 10-9 m.
- Calculate energy of one photon: E = hc/λ.
- Find energy for 5 moles: Etotal = E × (6.022 × 1023) × 5.