Microwave radiation is absorbed by the water in food. As the water absorbs the heat it causes the food to get hot. If the λ of a microwave is 10 cm, calculate the frequency of the microwave and the energy of each photon.
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To calculate the frequency (f) of the microwave radiation, we can use the formula:
c = λ * f
Where:
c = speed of light (approximately 3 × 10^8 m/s)
λ = wavelength
First, we need to convert the wavelength of the microwave radiation from centimeters to meters. Since 1 cm is equal to 0.01 m, the wavelength of the microwave radiation is:
λ = 10 cm * 0.01 m/cm = 0.1 m
Now, we can rearrange the formula to solve for the frequency:
f = c / λ
f = 3 × 10^8 m/s / 0.1 m
f = 3 × 10^9 Hz
The frequency of the microwave radiation is 3 × 10^9 Hz.
To calculate the energy of each photon (E), we can use the equation:
E = h * f
Where:
E = energy of each photon
h = Planck's constant (approximately 6.63 × 10^-34 J·s)
f = frequency
Plugging in the values:
E = (6.63 × 10^-34 J·s) * (3 × 10^9 Hz)
E ≈ 1.99 × 10^-24 J
Therefore, the energy of each photon in microwave radiation is approximately 1.99 × 10^-24 Joules.