Final answer:
To find the energy in joules per mole for a frequency of 7.39 × 10⁵ Hz, we use the equation E = hν with Planck's constant (6.626 × 10⁻³⁴ J·s) to first find the energy per photon, and then multiply by Avogadro's number to find the energy per mole, which is 2.948 × 10⁻⁴ J/mol.
Step-by-step explanation:
To calculate the energy in joules per mole for a frequency using Planck's constant, we can use the equation:
E = hν
Where E is the energy in joules, h is Planck's constant which is 6.626 × 10-34 joule-seconds (J·s), and ν (nu) is the frequency in hertz (Hz or s-1).
Given that the frequency is 7.39 × 105 Hz, we first find the energy for one photon:
E = (6.626 × 10-34 J·s) (7.39 × 105 Hz)
E = 4.897 × 10-28 J (per photon)
To find the energy per mole, we multiply this value by Avogadro's number (6.022 × 1023 mol-1):
Emole = (4.897 × 10-28 J) (6.022 × 1023 mol-1)
Emole = 2.948 × 10-4 J/mol
This is the energy in joules per mole for a frequency of 7.39 × 105 Hz.