Question

Your friend mentions to you that he never stands in front of the microwave oven while in use. The door to his oven has a grill with small holes, about 1mm in diameter, through which he is fearful that microwave radiation will leak and cause cancer. Most home microwave ovens oper- ate at a frequency of 2450 MHz. Cancer can be caused by ionizing radiation, with energies> 5- 10 eV/photon. (1 eV-6.02x10⁻¹⁹j)

a. What is the energy, in eV, of a single photon from your friends microwave?
b. What is the wavelength of that radiation, in millimeters? c. How do you respond to your friend's concern about radiation leakage?

Answer 1

The energy of a single photon from a microwave oven operating at 2450 MHz is approximately 2.69 x 10^-7 eV. The wavelength of that radiation is approximately 122 mm. Microwave ovens are designed with shielding to prevent significant radiation leakage, and the risk of microwave radiation causing cancer is very low.

Step-by-step explanation:

According to the information given, a microwave oven operates at a frequency of 2450 MHz. To find the energy of a single photon, we can use the equation E = hf, where h is Planck's constant (6.626 x 10^-34 J*s) and f is the frequency in Hz. Converting the frequency to Hz (2450 MHz = 2450 x 10^6 Hz) and plugging in the values, we have:

E = (6.626 x 10^-34 J*s)(2450 x 10^6 Hz) = 1.621 x 10^-26 J

Next, we can convert the energy to eV using the conversion factor given (1 eV = 6.02 x 10^-19 J):

E = (1.621 x 10^-26 J)/(6.02 x 10^-19 J/eV) ≈ 2.69 x 10^-7 eV.

The wavelength of the radiation can be found using the equation c = λf, where c is the speed of light (3 x 10^8 m/s), λ is the wavelength, and f is the frequency in Hz. Rearranging the equation to solve for λ, we have:

λ = c/f = (3 x 10^8 m/s)/(2450 x 10^6 Hz) ≈ 0.122 m = 122 mm.

In response to your friend's concern about radiation leakage, it is important to note that microwave ovens have shielding in place to prevent significant radiation from escaping. The grill with small holes on the oven door is designed to allow light to pass through while blocking most of the microwaves. In general, the risk of microwave radiation leakage from a properly functioning microwave oven is very low, and there is no evidence linking microwave ovens to cancer.