A single photon has an energy of 3.29 × 10^{-19} J. What is the wavelength of this photon in nanometers?

• A. 201 nm
• B. 452 nm
• C. 603 nm
• D. 987 nm

Answer: (C)

Verified step by step guidance

1. Recall the relationship between the energy of a photon and its wavelength, given by the equation: \(E = \frac{hc}{\lambda}\), 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. Identify the known values: Planck's constant \(h = 6.626 \times 10^{-34}\) J·s, speed of light \(c = 3.00 \times 10^{8}\) m/s, and the photon energy \(E = 3.29 \times 10^{-19}\) J.
3. Rearrange the equation to solve for the wavelength \(\lambda\): \(\lambda = \frac{hc}{E}\).
4. Substitute the known values into the rearranged equation: \(\lambda = \frac{(6.626 \times 10^{-34})(3.00 \times 10^{8})}{3.29 \times 10^{-19}}\).
5. Calculate \(\lambda\) in meters, then convert the result to nanometers by multiplying by \$10^{9}\( (since 1 m = \)10^{9}$ nm).