What is the energy, in kilojoules, of one mole of photons (an einstein) with a frequency of 8.23 × 10^{15} Hz? (Planck's constant, h = 6.626 × 10^{-34} J·s; Avogadro's number, N_A = 6.022 × 10^{23} mol^{-1})

• A. 5.47 × 10^{2} kJ
• B. 3.28 × 10^{6} kJ
• C. 4.92 × 10^{5} kJ
• D. 3.28 × 10^{3} kJ

Answer: (D)

Verified step by step guidance

1. Calculate the energy of a single photon using the formula \(E = h \times \nu\), where \(h\) is Planck's constant and \(\nu\) is the frequency of the photon. Substitute the given values: \(h = 6.626 \times 10^{-34}\) J·s and \(\nu = 8.23 \times 10^{15}\) Hz.
2. Multiply the energy of one photon by Avogadro's number \(N_A = 6.022 \times 10^{23}\) mol\(^{-1}\) to find the energy of one mole of photons (an einstein). This gives the total energy per mole in joules.
3. Convert the energy from joules to kilojoules by dividing the result by 1000, since 1 kJ = 1000 J.
4. Write the final answer in scientific notation to match the format of the given options.
5. Compare your calculated value with the provided options to identify the correct energy value in kilojoules per mole.