2. Use the Planck's equation to determine:
(a). The energy in joules per photon of radiation of frequency 7.39 × 1015 s-1.
(b). The energy in kilojoules per mole.
(a). The energy in joules per photon can be calculated using Planck's equation:
E = hf
where E is the energy, h is Planck's constant (6.626 × 10^-34 J·s), and f is the frequency of the radiation.
Plugging in the given frequency, we get:
E = (6.626 × 10^-34 J·s)(7.39 × 10^15 s^-1)
Calculating this, we find:
E ≈ 4.894 × 10^-18 J
Therefore, the energy in joules per photon of radiation with a frequency of 7.39 × 1015 s-1 is approximately 4.894 × 10^-18 J.
(b). To determine the energy in kilojoules per mole, we need to know the molar mass of the substance emitting the radiation. Let's assume we are talking about a substance with a molar mass of 1 gram/mole.
To convert the energy from joules to kilojoules, we divide by 1000:
4.894 × 10^-18 J ÷ 1000 = 4.894 × 10^-21 kJ
Now, to calculate the energy in kilojoules per mole, we need to convert from energy per photon to energy per mole. Since there are Avogadro's number of photons in 1 mole (6.022 × 10^23), we divide the energy per photon by Avogadro's number:
4.894 × 10^-21 kJ ÷ (6.022 × 10^23) = 8.127 × 10^-45 kJ/mol
Therefore, the energy in kilojoules per mole of radiation with a frequency of 7.39 × 1015 s-1 is approximately 8.127 × 10^-45 kJ/mol.