Given that the energy for a mole of photons is 1.55 × 10^{13} J, what is the frequency of the light? (Use Planck's constant h = 6.626 × 10^{-34} J·s and Avogadro's number N_A = 6.022 × 10^{23} mol^{-1})

• A. 1.56 × 10^{19} Hz
• B. 6.02 × 10^{23} Hz
• C. 2.34 × 10^{15} Hz
• D. 3.77 × 10^{12} Hz

Answer: (A)

Verified step by step guidance

1. Identify the given information: the energy for one mole of photons is \$1.55 \times 10^{13}\( J, Planck's constant \)h = 6.626 \times 10^{-34}\( J\cdot s, and Avogadro's number \)N_A = 6.022 \times 10^{23}\( mol\)^{-1}$.
2. Recall the relationship between the energy of a single photon and its frequency: \(E = h \nu\), where \(E\) is the energy of one photon and \(\nu\) is the frequency.
3. Since the given energy is for one mole of photons, calculate the energy of a single photon by dividing the total energy by Avogadro's number: \(E_{photon} = \frac{E_{mole}}{N_A}\).
4. Rearrange the photon energy formula to solve for frequency: \(\nu = \frac{E_{photon}}{h}\).
5. Substitute the values of \(E_{photon}\) and \(h\) into the equation to find the frequency \(\nu\) of the light.