Final answer:
The frequency of the photon produced when an electron in a hydrogen atom drops from the fifth energy level to the second energy level is ≈6.91x10¹⁴ Hz.
Step-by-step explanation:
When an electron in a hydrogen atom drops from the fifth energy level to the second energy level, releasing 4.58x10⁻¹⁹ J of energy, the frequency of the produced photon can be calculated using the Planck-Einstein relation: E = hf, where E is the energy, h is Planck's constant (6.626x10⁻³⁴ J·s), and f is the frequency of the photon.
To find the frequency, rearrange the equation to solve for f: f = E/h.
Plugging in the values, you get f = (4.58x10⁻¹⁹ J) / (6.626x10⁻³⁴ J·s) = 6.91x10¹⁴ Hz, which is the frequency of the photon emitted.