A particular microwave oven delivers 800 watts. (A watt is a...

A particular microwave oven delivers 800 watts. (A watt is a unit of power, which is the joules of energy delivered, or used, per second.) If the oven uses microwave radiation of wavelength $12.2 \mathrm{~cm}$, how many photons of this radiation are required to heat $1.00 \mathrm{~g}$ of water $1.00^{\circ} \mathrm{C}$, assuming that all of the photons are absorbed?

Key Concepts

Photon Energy

Photon energy is a concept in quantum mechanics where each photon, the basic unit of light, carries a discrete amount of energy. This energy is given by the relationship E = hc/?, where h is Planck’s constant, c is the speed of light, and ? is the wavelength of the photon. This concept is essential for understanding processes that involve the absorption or emission of light, particularly in contexts such as heating via electromagnetic radiation.

Planck's Equation

Planck's equation, E = hc/?, is a fundamental relation that connects the energy of a photon with its wavelength. It illustrates how energy is quantized and is crucial for calculations in various areas of modern physics and chemistry, including the analysis of radiation energy in microwave ovens or other types of electromagnetic radiation.

Microwave Radiation

Microwave radiation is a segment of the electromagnetic spectrum characterized by longer wavelengths compared to visible light. It is widely used in applications such as heating and communication because of its specific interactions with matter, particularly water molecules. This property makes microwave ovens effective for heating food through energy absorption by water.

Specific Heat Capacity

Specific heat capacity is the property of a substance that defines the amount of energy required to raise the temperature of a unit mass of the material by one degree Celsius. In problems involving heating, such as raising the temperature of water, this concept is used to calculate the total energy necessary for the desired temperature change.

Power

Power is defined as the rate at which energy is transferred or converted, measured in watts (joules per second). This concept is critical when relating the performance of an appliance, such as a microwave oven, to the overall energy delivery over time, thereby linking the macroscopic power consumption to microscopic energy processes like photon absorption.

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