To allow a family to listen to a radio station, a certain...

To allow a family to listen to a radio station, a certain home receiver must pick up a signal of at least
$1.0 \times 10^{-10} \mathrm{~W}$. If the radio waves have a frequency of
$96 \mathrm{MHz}$, how many photons must the receiver absorb per second to pick up the signal?

Key Concepts

Photon Energy

Photon energy is a fundamental concept in quantum mechanics that relates the energy carried by a photon to its frequency, expressed by the relation E = h f. This equation shows that as the frequency of electromagnetic radiation increases, so does the energy of each photon, linking microscopic particles of light with the macroscopic concept of energy.

Planck's Constant

Planck's constant is a universal constant that plays a critical role in quantum physics by setting the scale at which quantum effects become significant. It appears in the formula for photon energy (E = h f) and symbolizes the discrete nature of energy transfer, marking the boundary between classical and quantum descriptions.

Frequency

Frequency is the measurement of how many wave cycles pass a given point per unit of time and is a crucial characteristic of electromagnetic waves. In the context of photon energy, frequency determines the energy of each photon when multiplied by Planck's constant, thereby linking wave properties to particle behavior.

Power

Power is defined as the rate at which energy is transferred or converted, measured in watts. In problems involving energy absorption over time, power helps in determining the total energy received, which, when related to the energy per photon, allows for the calculation of how many photons are involved in the energy transfer.

Energy Quantization

Energy quantization is the concept that energy in certain systems, such as electromagnetic radiation, is not continuous but comes in discrete packets known as photons. This principle explains why energy transfer from an electromagnetic wave must occur in measurable, quantized amounts, linking classical power measurements to quantum levels.

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