How much energy (in kJ) do 4.50 moles of photons contain at a wavelength of 705 nm?

• A. 2.58 x 10² kJ
• B. 7.64 x 10² kJ
• C. 8.45 x 10² kJ
• D. 5.89 x 10² kJ

Answer: (B)

Verified step by step guidance

1. First, understand that the energy of a photon can be calculated using the equation: $E=\frac{\mathrm{hc}}{\lambda }$, where $h$ is Planck's constant ($6.626\; \times \; 10-34J·s$), $c$ is the speed of light ($3.00\; \times \; 108m/s$), and $\lambda$ is the wavelength in meters.
2. Convert the wavelength from nanometers to meters. Since 1 nm = 1 × 10^-9 m, the wavelength of 705 nm is $705\; \times \; 10-9m$.
3. Substitute the values of $h$, $c$, and $\lambda$ into the energy equation to find the energy of a single photon: $E=\frac{6.626\times {10}^{-34}\times 3.00\times {10}^8}{705\times {10}^{-9}}$.
4. Calculate the energy for 4.50 moles of photons. Since 1 mole contains $6.022\; \times \; 1023$ photons (Avogadro's number), multiply the energy of one photon by $4.50\; \times \; 6.022\; \times \; 1023$.
5. Convert the total energy from joules to kilojoules by dividing by 1000, as 1 kJ = 1000 J. This will give you the energy in kJ for 4.50 moles of photons.