What is the energy, in joules, of a single photon with a wavelength of 347 nm?

• A. 1.92 × 10^{-16} J
• B. 8.56 × 10^{-21} J
• C. 3.45 × 10^{-18} J
• D. 5.73 × 10^{-19} J

Answer: (D)

Verified step by step guidance

1. Identify the formula that relates the energy of a photon to its wavelength: \(E = \frac{hc}{\lambda}\), where \(E\) is the energy of the photon, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.
2. Write down the known constants: Planck's constant \(h = 6.626 \times 10^{-34}\) J·s, and the speed of light \(c = 3.00 \times 10^{8}\) m/s.
3. Convert the wavelength from nanometers to meters because SI units must be consistent: \$347\( nm \)= 347 \times 10^{-9}$ m.
4. Substitute the values into the formula: \(E = \frac{(6.626 \times 10^{-34})(3.00 \times 10^{8})}{347 \times 10^{-9}}\).
5. Perform the division and multiplication to find the energy \(E\) in joules, which will give the energy of a single photon with the given wavelength.