How much energy (in kJ) do 3.0 moles of photons, all with a wavelength of 655 nm, contain?

• A. 912 kJ
• B. 1200 kJ
• C. 750 kJ
• D. 550 kJ

Answer: (A)

Verified step by step guidance

1. First, understand that the energy of a photon can be calculated using the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy of a photon, \( h \) is Planck's constant \( (6.626 \times 10^{-34} \text{ J s}) \), \( c \) is the speed of light \( (3.00 \times 10^8 \text{ m/s}) \), and \( \lambda \) is the wavelength in meters.
2. Convert the given wavelength from nanometers to meters. Since 1 nm = \( 1 \times 10^{-9} \) m, the wavelength \( \lambda = 655 \text{ nm} \) is equivalent to \( 655 \times 10^{-9} \text{ m} \).
3. Substitute the values of \( h \), \( c \), and \( \lambda \) into the energy equation to find the energy of a single photon: \( E = \frac{(6.626 \times 10^{-34} \text{ J s})(3.00 \times 10^8 \text{ m/s})}{655 \times 10^{-9} \text{ m}} \).
4. Calculate the energy for one photon using the above expression. This will give you the energy in joules for one photon.
5. To find the total energy for 3.0 moles of photons, multiply the energy of one photon by Avogadro's number \( (6.022 \times 10^{23} \text{ photons/mole}) \) and then by 3.0 moles. Convert the result from joules to kilojoules by dividing by 1000.