What is the energy in kJ/mol of photons with a wavelength of 450 nm?

• A. 150 kJ/mol
• B. 350 kJ/mol
• C. 500 kJ/mol
• D. 265 kJ/mol

Answer: (D)

Verified step by step guidance

1. First, understand the relationship between energy and wavelength. The energy of a photon can be calculated using the equation: E = \( \frac{hc}{\lambda} \), where E is the energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and \( \lambda \) is the wavelength.
2. Convert the wavelength from nanometers to meters. Since 1 nm = 1 x 10^-9 m, a wavelength of 450 nm is equivalent to 450 x 10^-9 m.
3. Substitute the values into the equation: E = \( \frac{(6.626 \times 10^{-34} \text{ J·s})(3.00 \times 10^8 \text{ m/s})}{450 \times 10^{-9} \text{ m}} \). This will give you the energy of a single photon in joules.
4. Convert the energy from joules per photon to kilojoules per mole. Use Avogadro's number (6.022 x 10^23 mol^-1) to find the energy per mole: \( E_{\text{kJ/mol}} = \frac{E_{\text{J/photon}} \times 6.022 \times 10^{23}}{1000} \).
5. Finally, compare the calculated energy value to the given options to identify the correct answer.