A photon has an energy of 3.9 × 10^{-18} J. What is its wavelength?

• A. 3.2 × 10^{-9} m
• B. 1.2 × 10^{-10} m
• C. 7.6 × 10^{-6} m
• D. 5.1 × 10^{-7} m

Answer: (D)

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, \(h\) is Planck's constant, \(c\) is the speed of light, and \(\lambda\) is the wavelength.
2. Identify the known values: the energy \(E = 3.9 \times 10^{-18}\) J, 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. Rearrange the equation to solve for the wavelength \(\lambda\): \(\lambda = \frac{hc}{E}\).
4. Substitute the known values into the rearranged equation: \(\lambda = \frac{(6.626 \times 10^{-34})(3.00 \times 10^{8})}{3.9 \times 10^{-18}}\).
5. Perform the calculation to find the wavelength \(\lambda\), which will give the photon's wavelength in meters.