Enormous numbers of microwave photons are needed to warm...

Enormous numbers of microwave photons are needed to warm macroscopic samples of matter. A portion of soup containing $252 \mathrm{~g}$ of water is heated in a microwave oven from $20 .^{\circ} \mathrm{C}$ to $98^{\circ} \mathrm{C}$, with radiation of wavelength $1.55 \times 10^{-2} \mathrm{~m}$. How many photons are absorbed by the water in the soup?

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Key Concepts

Planck’s Relation

This concept connects the energy of a photon with its wavelength using the equation E = hc/?, where h is Planck’s constant and c is the speed of light. It is fundamental in determining the energy carried by electromagnetic radiation of a specific wavelength.

Specific Heat Capacity

Specific heat capacity is the amount of energy required to raise the temperature of a unit mass of a substance by one degree Celsius. This concept is used to calculate the total energy needed to heat a given mass of a substance over a certain temperature change.

Energy Conversion from Photons to Thermal Energy

This concept involves translating the total thermal energy required for heating into the number of photons needed, by dividing the necessary thermal energy by the energy per photon. It bridges the gap between macroscopic thermal processes and the microscopic energy of individual photons.

Microwave Radiation

Microwave radiation is a form of electromagnetic energy with wavelengths typically in the range of centimeters to millimeters. Understanding its properties, such as wavelength and frequency, is essential when calculating photon energy in applications like microwave heating.

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