Final answer:
To find the wavelength of a photon with an energy of 2 eV, we use the relationship E = hc/λ, convert the energy to joules, and solve for wavelength, to get that the closest wavelength is 620 nm.
Step-by-step explanation:
The question deals with finding the wavelength of a photon given its energy in electron volts (eV). The energy of a photon is related to its wavelength by the equation E = hc/λ, where E is the energy of the photon, h is Planck's constant (6.626 x 10-34 J·s), c is the speed of light in a vacuum (approximately 3.00 x 108 m/s), and λ is the wavelength of the photon. We want to convert the given energy of 2 eV to joules first, and using the conversion factor 1 eV = 1.602 x 10-19 J. Then, we will be able to solve for the wavelength in meters and convert to nanometers for the final answer.
First, we convert the photon's energy to joules: 2 eV * 1.602 x 10-19 J/eV = 3.204 x 10-19 J. Inserting this into the energy-wavelength relationship and solving for λ gives:
λ = hc/E = (6.626 x 10-34 J·s)(3.00 x 108 m/s) / (3.204 x 10-19 J) ≈ 620 nm. Therefore, the closest wavelength to a photon with an energy of 2 eV is 620 nm (option b).