Final answer:
To calculate the wavelength of a photon with an energy of 2.05 eV, we use the energy-wavelength relationship with Planck's constant and the speed of light. After converting eV to joules and substituting the values into the formula, we find a wavelength of approximately 603.94 nm, making the closest answer (c) 650 nm.
Step-by-step explanation:
To find the wavelength of a single photon given its energy, you can use the formula that relates a photon's energy (E) to its wavelength (λ) through Planck's constant (h) and the speed of light (c):
E = (h * c) / λ
First, we need to convert the energy from electron volts to joules since Planck's constant is given in joules·seconds. The conversion factor is 1 eV = 1.602 x 10-19 J. Thus, an energy of 2.05 eV is equivalent to 2.05 * 1.602 x 10-19 J. Next, using Planck's constant (h = 6.626 x 10-34 js) and the speed of light (c = 3.00 x 108 m/s), we can rearrange the formula to solve for λ:
λ = (h * c) / E
Substituting the values, we find the wavelength:
λ = (6.626 x 10-34 js * 3.00 x 108 m/s) / (2.05 * 1.602 x 10-19 J) = 603.94 nm.