Final answer:
The frequency of a photon with energy of 0.0139 eV is approximately 3.37 × 10¹² Hz, calculated using Planck's equation and conversion from eV to J.
Step-by-step explanation:
To calculate the frequency of a photon with a given energy, we can use Planck's equation, which relates the energy (E) of a photon to its frequency (ƒ) by the formula E = hƒ, where h is Planck's constant (6.626 × 10−34 J·s). First, we need to convert the energy from electronvolts (eV) to joules (J) using the conversion factor where 1 eV = 1.602 × 10−19 J. With an energy of 0.0139 eV, we have:
E = 0.0139 eV × (1.602 × 10−19 J/eV) = 2.22778 × 10−20 J
Now we solve for frequency (ƒ):
ƒ = E / h = (2.22778 × 10−20 J)/(6.626 × 10−34 J·s) ≈ 3.37 × 1012 Hz
Therefore, the frequency of a photon with an energy of 0.0139 eV is approximately 3.37 × 1012 Hz, which corresponds to answer choice B.