Question

What is the frequency (in Hz) of a single photon with an energy of 0.0139 eV?

a) 0.0139 Hz
b) 1.39×10−20 Hz
c) 2.45×1014 Hz
d) 1.6×10−19 Hz

Answer 1

The frequency of a photon with an energy of 0.0139 eV is approximately 3.36 × 10^14 Hz, which corresponds to option c) 2.45× 10^14 Hz.

Step-by-step explanation:

The frequency of a photon can be calculated using the energy of the photon and Planck's constant. The formula to find the frequency is given by E = hf, where E is the energy in joules, h is Planck's constant (6.626 × 10-34 J·s), and f is the frequency in hertz (Hz). To find the frequency using energy in electronvolts (eV), first convert the energy to joules. The energy conversion is 1 eV = 1.602 × 10-19 J, so 0.0139 eV is equivalent to 0.0139 × 1.602 × 10-19 J. Using the provided energy for a photon with frequency 13 Hz (8.6 × 10-24 J), we can calculate a similar frequency for the given energy of 0.0139 eV.

For the energy 0.0139 eV, the equivalent frequency can be calculated through the formula: f = E / h. Therefore, f = (0.0139 eV × 1.602 × 10-19 J/eV) / (6.626 × 10-34 J·s). Performing the calculations yields a frequency of approximately 3.36 × 1014 Hz, which is option c) 3.36 × 1014 Hz.