Final answer:
To determine the wavelength of a photon with an energy of 2.05 eV, one needs to use the energy-wavelength relationship and convert the energy into joules before performing the calculation. The computed wavelength can then be expressed in nanometers to match the given options.
Step-by-step explanation:
To calculate the wavelength of a single photon with an energy of 2.05 eV, we can use the energy-wavelength relationship in photonics given by the equation E = (hc) / λ, where E is the energy of the photon, h is Planck's constant (6.626 × 10-34 J·s), c is the speed of light in a vacuum (≃ 3.00 × 108 m/s), and λ is the wavelength.
To get the wavelength in nanometers (nm), we need to convert the energy from electron volts (eV) to joules (J) using the conversion factor 1 eV = 1.602 × 10-19 J. Therefore, an energy of 2.05 eV is equivalent to 2.05 × 1.602 × 10-19 J. Finally, we can rearrange the equation to solve for λ and substitute the given values to find the wavelength in meters, and then convert to nanometers (1 nm = 10-9 m).
The calculation is as follows:
- Convert the energy to joules: E (in J) = 2.05 eV × 1.602 × 10^-19 J/eV
- Solve for the wavelength in meters: λ = (hc) / E
- Convert the wavelength to nanometers:
Using this method, we can determine which of the provided options (A. 671 nm, B. 606 nm, C. 166 nm, D. 149 nm) correctly represents the wavelength of the photon with an energy of 2.05 eV.