What is the energy (in kJ) of one mole of photons with wavelength λ = 720 nm?

• A. 418 kJ
• B. 166 kJ
• C. 249 kJ
• D. 333 kJ

Answer: (B)

Verified step by step guidance

1. Identify the given information: the wavelength of the photons is \( \lambda = 720 \text{ nm} \). Convert this wavelength into meters by using the conversion \( 1 \text{ nm} = 1 \times 10^{-9} \text{ m} \).
2. Recall the formula to calculate the energy of a single photon: \[ E = \frac{hc}{\lambda} \] where \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \text{ J} \cdot \text{s} \)) and \( c \) is the speed of light (\( 3.00 \times 10^{8} \text{ m/s} \)).
3. Calculate the energy of one photon by substituting the values of \( h \), \( c \), and \( \lambda \) (in meters) into the formula.
4. Since the question asks for the energy of one mole of photons, multiply the energy of one photon by Avogadro's number \( N_A = 6.022 \times 10^{23} \) photons/mole: \[ E_{\text{mole}} = E \times N_A \].
5. Convert the energy from joules to kilojoules by dividing by 1000, because 1 kJ = 1000 J, to express the final answer in kJ/mol.