Final answer:
To calculate the energy of an IR photon, use the Planck-Einstein relation E = h⋅f, with Planck's constant and the given frequency. Convert the result from joules to electron volts to find the energy in eV. The energy is approximately (1.32 × 10^-5) eV.
Step-by-step explanation:
To calculate the energy E in electron volts (eV) of an infrared (IR) photon with a given frequency, we use the Planck-Einstein relation:
E = h⋅f,
where h is Planck’s constant and f is the frequency of the photon. Since the energy units required are in electron volts and Planck’s constant is typically given in joules, we will need to convert the energy from joules to electron volts. The value of Planck's constant is 6.626×10-34 J⋅s and the value of the charge of an electron is 1.602×10-19 C (or joules per eV).
Using the given frequency of 2.00 × 1013 Hz, the energy in joules is calculated first:
E = (6.626 × 10-34 J⋅s)(2.00 × 1013 Hz) = 1.3252 × 10-20 J.
To convert to electron volts, we divide by the charge of an electron:
E = 1.3252 × 10-20 J / (1.602 × 10-19 C/eV) = 0.0827 eV.
Therefore, the correct answer is approximately (a) (1.32 × 10-5) eV.