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
To answer these questions, we need to use the formula:
wavelength (λ) = speed of light (c) / frequency (f)
The speed of light is a constant value of approximately 3.00 x 10^8 meters per second (m/s). However, it is important to convert the frequency from megahertz (MHz) to hertz (Hz) by multiplying it by 10^6.
a. What is the wavelength of the microwaves used in this microwave oven?
First, convert the frequency from 2,450 MHz to Hz:
2,450 MHz = 2,450 x 10^6 Hz
Substituting the values into the formula:
wavelength (λ) = 3.00 x 10^8 m/s / (2,450 x 10^6 Hz)
wavelength (λ) = 0.1224 meters (or 12.24 centimeters)
Therefore, the wavelength of the microwaves used in this microwave oven is approximately 0.1224 meters (or 12.24 centimeters).
b. What is the energy per quantum of this microwave oven?
The energy per quantum of electromagnetic radiation can be calculated using the equation:
Energy (E) = Planck's constant (h) x frequency (f)
Planck's constant is a fundamental physical constant with a value of approximately 6.63 x 10^-34 Joule seconds (J·s).
Substituting the values into the equation:
Energy (E) = 6.63 x 10^-34 J·s x 2,450 x 10^6 Hz
Energy (E) = 1.61775 x 10^-26 Joules (J)
Therefore, the energy per quantum of this microwave oven is approximately 1.61775 x 10^-26 Joules (J).
c. How many quanta of 2,450 MHz microwave energy are in 1.00 J of energy?
To find the number of quanta, we need to divide the total energy (1.00 J) by the energy per quantum (1.61775 x 10^-26 J):
Number of quanta = 1.00 J / 1.61775 x 10^-26 J
Number of quanta ≈ 6.18 x 10^25 quanta
Therefore, there are approximately 6.18 x 10^25 quanta of 2,450 MHz microwave energy in 1.00 J of energy.