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Multiple Choice
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
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.
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.
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.
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: \( E_{\text{kJ/mol}} = \frac{E_{\text{J/photon}} \times 6.022 \times 10^{23}}{1000} \).
Finally, compare the calculated energy value to the given options to identify the correct answer.