An FM radio station broadcasts at a frequency of 89.3 MHz....

An FM radio station broadcasts at a frequency of $89.3$ MHz. The power radiated from the antenna is $50.0 \mathrm{~kW}$. (a) What is the energy in eV of each photon radiated by the antenna? (b) How many photons per second does the antenna emit?

Key Concepts

Unit Conversion (Joules to Electron Volts)

Often in physics, especially in quantum mechanics, energy is expressed in electron volts (eV). Converting energy from joules to electron volts involves using the conversion factor (1 eV = 1.602 x 10^-19 joules). Mastery of unit conversions is crucial to correctly interpret and compare energy scales in different contexts.

Power and Energy per Time Relationship

Power is defined as the rate at which energy is emitted, transferred, or consumed. In the context of radiated energy, the number of photons emitted per second can be calculated by dividing the total power (energy per unit time) by the energy of one photon. This relationship is key to linking macroscopic measures such as power with microscopic events such as photon emission.

Photon Energy (Planck’s Equation)

This concept involves calculating the energy of a photon using the relation E = h·f, where h is Planck's constant and f is the frequency of the electromagnetic wave. This fundamental relation connects the wave nature of light with its particle properties and is central in quantum mechanics and electromagnetic theory.

Electromagnetic Spectrum and Frequency

Understanding the relationship between frequency and the type of electromagnetic radiation is key. The energy of a photon is directly proportional to its frequency, which means that for any electromagnetic radiation, knowing its frequency allows one to determine the energy per photon. This concept is applicable across the spectrum from radio waves to gamma rays.

Transcript

Please give Ace some feedback