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?
speed of light/frequency = 3 * 10^8/ 2,450 = 122448.98 (help units)
b. What is the energy per quantum of this microwave oven?
2,450 times planck's constant = 3.9772985^-27 (help w/ units)
c. How many quanta of 2,450 MHz.microwave energy are in 1.00 J of energy
1/3.9772985^-7 (units?)
a. (3.0E10 cm/s) / 2.45E9 hz = 12 cm
b. 2.45E9 hz * 6.63E-34 J⋅s = 1.68E-24 J
c. 1 / 1.68E-24 = 5.95E23 quanta
thanks! :) you helped me alot.
a. To find the wavelength of the microwaves used in the microwave oven, you can use the formula:
Wavelength = Speed of Light / Frequency
Given that the frequency is 2,450 MHz (which is equivalent to 2,450 * 10^6 Hz) and the speed of light is approximately 3 * 10^8 m/s, you can substitute these values into the formula:
Wavelength = (3 * 10^8 m/s) / (2,450 * 10^6 Hz)
Now, you can simplify the equation and calculate the wavelength:
Wavelength = 122448.98 m (meters)
Therefore, the wavelength of the microwaves used in this microwave oven is approximately 122448.98 meters.
b. The energy per quantum of the microwave oven can be found using the equation:
Energy per Quantum = Frequency * Planck's Constant
Given that the frequency is 2,450 MHz (which is equivalent to 2,450 * 10^6 Hz) and Planck's constant is approximately 6.62607015 * 10^-34 J·s, you can substitute these values into the formula:
Energy per Quantum = (2,450 * 10^6 Hz) * (6.62607015 * 10^-34 J·s)
Now, you can simplify the equation and calculate the energy per quantum:
Energy per Quantum = 3.9772985 * 10^-27 J (joules)
Therefore, the energy per quantum of this microwave oven is approximately 3.9772985 * 10^-27 joules.
c. To find the number of quanta of 2,450 MHz microwave energy in 1.00 J of energy, you can use the equation:
Number of Quanta = Total Energy / Energy per Quantum
Given that the total energy is 1.00 J and the energy per quantum is 3.9772985 * 10^-27 J (as found in part b), you can substitute these values into the formula:
Number of Quanta = 1.00 J / 3.9772985 * 10^-27 J
Now, you can simplify the equation and calculate the number of quanta:
Number of Quanta = 2.51416 * 10^26 quanta (quanta)
Therefore, there are approximately 2.51416 * 10^26 quanta of 2,450 MHz microwave energy in 1.00 J of energy.