microwave ovens work by irradiating food with microwaves, which is absorbed by the water molecules in the food and is converted into heat. Assuming that microwave ovens emit radiation with a wavelength of 12.2cm, calculate how many photons are emitted per second in a 1000-Watt microwave oven.
1000/(1.6*10^-24) =
6.25*10^26 photons/sec
1000 watts = 1000 joules/second
E = hc/wavelength
E = 6.626E-34*3E8/12.2E-2 for one photon.
1.6E-24 J/photon x # photons = 1000 joules/sec.
Solve for # photons.
To calculate the number of photons emitted per second in a 1000-Watt microwave oven, we need to use the formula that relates energy, power, and frequency of the radiation.
The formula we're going to use is:
E = hf
Where:
E represents energy,
h represents Planck's constant (6.626 x 10^-34 Js),
and f represents the frequency of the radiation.
First, we need to calculate the frequency (f) using the formula:
v = fλ
Where:
v represents the speed of light (3 x 10^8 m/s)
and λ represents the wavelength of the radiation.
Converting the wavelength of 12.2 cm (0.122 m), we can write:
0.122 m = (3 x 10^8 m/s) × f
Rearranging the equation to solve for frequency (f), we get:
f = 0.122 m / (3 x 10^8 m/s)
f ≈ 4.07 x 10^8 Hz
Now that we have the frequency, we can calculate the energy of a single photon using the equation E = hf:
E = (6.626 x 10^-34 Js) × (4.07 x 10^8 Hz)
E ≈ 2.695 x 10^-25 J
Next, we'll calculate the number of photons per second emitted by a 1000-Watt microwave oven.
Since power is the rate at which energy is emitted, we divide the power (P) by the energy per photon (E):
Number of photons emitted per second = Power / Energy per photon
Number of photons emitted per second = 1000 / (2.695 x 10^-25)
Number of photons emitted per second ≈ 3.71 x 10^24 photons
Therefore, a 1000-Watt microwave oven emits approximately 3.71 x 10^24 photons per second.