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Microwave radiation is a type of electromagnetic radiation with wavelengths ranging from one meter to one millimeter, or equivalently, with frequencies between 300 MHz (0.3 GHz) and 300 GHz.
This makes them longer than infrared rays but shorter than radio waves. Microwaves are best known for their use in microwave ovens where they are used to heat food. The microwaves cause water molecules within food to vibrate, creating thermal energy that heats the food.
In the context of the exercise, the microwave oven emits microwave radiation to heat a small amount of water.

• This radiation is characterized by a wavelength—in this case, 12.2 cm—which is within the typical range for microwave ovens.
• The energy delivered by this microwave oven is measured in watts. For this example, the oven delivers 800 watts, which means it provides 800 joules of energy every second.

Understanding how microwaves work helps explain how energy is transferred to food or water in this appliance.

Specific heat capacity is a measure of the amount of heat necessary to change the temperature of a substance by a certain amount.
For water, the specific heat capacity is 4.18 joules per gram per degree Celsius (J/g°C). This means that to raise the temperature of 1 gram of water by 1°C, it requires 4.18 joules of energy.

• This value is relatively high compared to other substances, which is why water is excellent for thermal regulation and storage.
• In the exercise, this concept helps calculate the total energy needed to heat water by determining the amount of heat required to raise its temperature by a specific degree.

This calculation is crucial in determining how many photons are needed to deliver this energy, illustrating the relationship between macroscopic energy needs and microscopic photon energy calculations.

Frequency and wavelength are fundamental parameters of waves that are inversely related.
They are connected by the speed of light in a vacuum ef The equation connecting them is \( c = \lambda u \), where:

• \( c \) is the speed of light \( \approx 3.00 \times 10^8 \text{ m/s} \)
• \( \lambda \) is the wavelength
• \( u \) (nu) is the frequency

The exercise involves converting the wavelength of the microwave radiation to its equivalent frequency:

• First, the wavelength is converted from centimeters to meters for consistency with the units of the speed of light.
• Then, frequency is found by rearranging the equation to \( u = \frac{c}{\lambda} \).
• The calculated frequency is vital for finding the energy of individual photons using another important constant, Planck's constant.

Understanding this conversion aids in creating the necessary bridge between macroscopic energy understanding and the behavior of photons.

Planck's constant \( h \) is a fundamental constant that quantifies the relationship between the frequency of a photon and its energy.
The value of Planck's constant is \( 6.626 \times 10^{-34} \text{ J}\cdot\text{s} \).

• It serves as a bridge between the macroscopic and quantum worlds, linking quantum mechanical and classical physical properties.
• The energy \( E \) of a photon is given by the equation \( E = h u \). This illustrates that higher frequency photons have more energy.

In the context of the exercise, Planck's constant is used to calculate the energy of a single photon at a specific microwave radiation frequency:

• First, the frequency calculated is inserted into the equation \( E = h u \).
• The resultant energy of a single photon can then be used to determine how many such photons are needed to provide the energy required to heat the water.

Recognizing Planck's constant's role in energy calculations is key to understanding energy quantization in quantum physics and acts as an essential component in photon energy calculations.