What is the energy in joules associated with a mole of photons that have a wavelength of 325 nm?

• A. 6.12 x 10^5 J
• B. 3.68 x 10^5 J
• C. 3.68 x 10^-19 J
• D. 6.12 x 10^-19 J

Answer: (B)

Verified step by step guidance

1. Start by understanding the relationship between energy and wavelength. The energy of a photon can be calculated using the formula: $E=\frac{\mathrm{hc}}{\lambda }$, where $h$ is Planck's constant ($6.626\; x\; 10-34Js$), $c$ is the speed of light ($3.00\; x\; 108m/s$), and $\lambda$ is the wavelength in meters.
2. Convert the wavelength from nanometers to meters. Since 1 nm = $1\; x\; 10-9m$, the wavelength of 325 nm can be converted to meters by multiplying by $1\; x\; 10-9$.
3. Substitute the values of $h$, $c$, and $\lambda$ into the energy formula to calculate the energy of a single photon: $E=\frac{6.626\times {10}^{-34}\times 3.00\times {10}^8}{325\times {10}^{-9}}$.
4. To find the energy associated with a mole of photons, multiply the energy of a single photon by Avogadro's number ($6.022\; x\; 1023$), which represents the number of photons in one mole.
5. The result from the previous step will give you the energy in joules for a mole of photons with a wavelength of 325 nm. Ensure that all units are consistent and correctly converted throughout the calculation.