A popular kitchen appliance produces electromagnetic radiation with a frequency of 2450 MHz. With reference to Figure 6.4, answer the following: (b) Would the radiation produced by the appliance be visible to the human eye?

Video transcript

Hey everyone, we're told that a certain medical procedure requires a patient to be temporarily exposed to radiation with the frequency of 27.12 MHz referring to the figure below, is this radiation visible to the naked eye. If this radiation is actually visible to the naked eye, then we would see it within our visible spectrum. So let's go ahead and figure that out First. We want to convert our 27.12 MHz into hurts so we can compare it and use it in our calculations later on. Now per one megahertz, we know that we have 10 to the six hertz. So when we calculate that out, we end up with 2.712 times 10 to the negative seven hertz. Now let's go ahead and calculate our wavelength in order to determine if it is part of our visible spectrum. As we've learned, we know that our speed of light is equivalent to our wavelength times our frequency. And if we rearrange that equation to solve for wavelength, we end up with speed of light divided by frequency. Now, plugging in those values, we get 3.0 times 10 to the eight m/s, divided by a frequency of 2.712 times 10 to the negative seven hertz, which can also be written as second to the negative first. Now, when we calculate this out and cancel out our unit, we end up with 11.06 m, which will essentially be in this section right here. So this means that we are in our radio waves and as we can see our figure, radio waves are not part of the visible spectrum. So our answer here is going to be the radiation is not visible to the naked eye, and this is going to be our final answer. Now. I hope that made sense and let us know if you have any questions.