4. A microwave oven uses an electronic device called a magnetron to produce microwaves. Microwaves
commonly used in ovens have a frequency of 2,450 MHz. (MHz = 106 Hz) The microwaves then pass into
the enclosed metal oven cavity where they are reflected around the oven walls and absorbed by food or drink placed in the oven. This is how microwave ovens heat food.
a. What is the wavelength of the microwaves used in this microwave oven?
b. What is the energy per quantum of this microwave oven?
c. How many quanta of 2,450 MHz.microwave energy are in 1.00 J of energy
a. wavelength = speed of light / frequency = (3E10 cm/s) / 2.45E9 hz
b. energy = frequency * Planck's constant
c. divide 1.00 J by the result in b.
What is Planck's constant?
6.62607004 × 10-34 m2 kg / s
a. To find the wavelength of the microwaves used in the microwave oven, you can use the formula:
Wavelength = Speed of Light / Frequency
The speed of light is a constant value represented as "c" which is approximately 3 x 10^8 meters per second. In this case, the frequency is given as 2,450 MHz, which can be converted to hertz by multiplying by 10^6. So the frequency is 2,450 x 10^6 Hz.
Plugging these values into the formula, we get:
Wavelength = (3 x 10^8 m/s) / (2,450 x 10^6 Hz)
Simplifying the numbers, the wavelength of the microwaves used in the microwave oven is approximately 0.122 meters or 12.2 centimeters.
b. The energy per quantum of the microwave oven can be calculated using Planck's equation:
Energy = Planck's constant * Frequency
Planck's constant is a fundamental constant represented as "h", which is approximately 6.626 x 10^-34 joule-seconds. The frequency in this case is 2,450 x 10^6 Hz.
Plugging these values into the equation, we get:
Energy = (6.626 x 10^-34 J s) * (2,450 x 10^6 Hz)
Simplifying the numbers, the energy per quantum of this microwave oven is approximately 1.62 x 10^-24 joules.
c. To determine how many quanta of 2,450 MHz microwave energy are in 1.00 J of energy, you can divide the total energy by the energy per quantum. In this case, we divide 1.00 J by the energy per quantum we calculated in part b (1.62 x 10^-24 J).
Number of quanta = 1.00 J / (1.62 x 10^-24 J)
Simplifying the calculation, we find that there are approximately 6.17 x 10^23 quanta of 2,450 MHz microwave energy in 1.00 J of energy.