List these types of electromagnetic radiation in order of (i) increasing frequency and (ii) decreasing energy per photon. a. gamma rays b. radio waves c. microwaves d. visible light

Video transcript

hey everyone in this example, we're given the below waves and we have a two part question. We're in part one, we need to list these waves from lower to higher energy. And then in part two we need to list the waves from higher to lower frequency. So we want to recall our formula for energy and we should recall that energy is equal to Planck's constant, multiplied by the frequency. So what we should simplify this relationship too is because both energy and frequency R in the numerator of our formula, we can say that energy is directly related to frequency. And so for example, if our energy of our wave is increasing, so is our frequency because they are directly related. Now our next step um To answer this question is to sketch our electromagnetic spectrum and we want to recall that this is a diagram that's going to show us exactly where our waves are occurring and at what magnitude they're occurring at as well as at what frequency. So the start of our spectrum is going to begin with waves that our that are super long in magnitude and super long in their wavelength. And then our waves are going to progressively become a bit smaller in magnitude where they're going to become a lot shorter in their wavelength. And as this continues on our spectrum, our waves are going to become even more dense and shorter in magnitude. To the point where we have such short and dense waves that our spectrum comes to an end and at each of these different points of our spectrum, we're going to list the types of waves we encounter. So at the start of our spectrum we want to take note of the fact that we have different magnitudes as far as our wavelength. That will be. We will be listing below. We want to recall that the symbol for wavelength is our lambda symbol and that's going to be measured in units of meters. And our second measurement that we're going to label on our diagram here is going to be our frequency. We should recall that our frequency symbol is a symbol as we wrote above and that is normally in units of hurts. So we'll start our magnitude listing by putting the following wavelength measures where we begin our spectrum at around 10 to the fifth power meters And continue on to about 10 to the negative first power m where we encompass our first type of wave and that's going to be our radio waves. And as you can see, we have a very long distance between our radio waves because they are at such a great magnitude. And as you can see, because our spectrum is going to continue to create waves that are smaller in magnitude and shorter in distance. We can already see that our exponents in our wavelength measure is already becoming smaller and more negative. Now, as far as our frequency of these types of radio waves, this is going to occur at the range of 10 to the third power hurts and 10 to the eighth power hurts. So at this at these frequency ranges we will encounter are radio waves on our electromagnetic spectrum. So now we're just going to continue on and write out our next wave length measure, which occurs at around 10 to the negative third power m. And at this point we should be listing our microwave rays. So this is going to continue to about 10 to the negative 5th power m. Where we have our second measurement here and Listing down the frequencies below, we would go ahead and write out that 10 to the 12th power Hertz is where our microwave waves should begin on our spectrum. And what we can already notice is that as our wavelength becomes smaller in magnitude because we see the exponents becoming more negative. We see our frequency on the other hand is becoming greater in magnitude because we have more positive and larger exponents as we continue down our spectrum of our waves. And so that would make sense that our frequency is becoming bigger because our waves are being created faster and so they're becoming a lot shorter in distance and smaller in magnitude. So our next step is to list where our infrared waves will occur. And that is actually at the point where our unit of measure 10 to the negative fifth power meters for our wavelength is listed here. So infrared waves would begin at this magnitude. Now following infrared waves, we want to list our next magnitude specifically at 7.8 times 10 to the negative seven power meters. And this is characterizing where our visible light is ready to be seen. And we wrote down specifically 7.8 times 10 to the negative seven power meters because we would convert that to 780 nanometers. And this is going to correspond to our human eye. Being able to see the ruby red spectrum of our visible light waves, which will occur at exactly 7 80 nanometers. And as far as our frequency here, this is going to be characterized at around 10 to the 15th power hurts. So then we're going to write in our next magnitude which is specifically at 3.9 times 10 to the negative seven power meters. And when we convert that to nanometers, that's going to correspond to 390 nanometers, which is actually where the last part of our visible light spectrum is occurring at a very violent tone here. And after this unit of measure, we're going to proceed to our next magnitude which occurs at 10 to the negative eight m. And this is where we can say we have our UV light occurring. And so UV ultraviolet light we want to recall is so violent and so bright that it is not visible to our human eye. And so this would make sense because at this point our waves are past the point of visible light and they're super small in magnitude. They're super short in distance and as far as the frequency of these waves, this would occur at around 10 to the 16th. Power hurts. Next we're going to begin the range from 10 to the negative eight power meters up to the point of 10 to the negative 12 power meters. And this is going to characterize and I'm just going to make our spectrum a teeny bit longer here. This is going to characterize the point where we hit our second to last type of wave, which is known as our x rays. So at this point we can see we have a very small and negative exponents here 10 times to the negative 12. So this would make sense that our waves are super dense and super small in magnitude. So this is going to correspond to 10 to the 20th. Power hurts as our frequency of these waves, which is why they are occurring at such a fast rate and creating these small, super dense waves. And lastly we're just going to place an arrow that continues towards the end of our spectrum because anything past the point of 10 to the negative 12 power meters is going to characterize our gamma race. And so these gamma rays are occurring at such a high frequency which is anything greater than 10 to the 20th power hurts. And at such a small wavelength that it's ending off our spectrum and creating these or the shortest type of wavelength here at the smallest magnitude. And so now we have fully outlined our electromagnetic spectrum. We can use the information in the spectrum to answer both parts of our question. So again above we pointed out the fact that energy and frequency are directly related to one another so that as energy is increasing, frequency is also going to be increasing. And according to our electromagnetic spectrum, we labeled frequency in units of hurts And we would agree that at the end of our spectrum, where are gamma rays occur. We have a super high frequency value past anything past 10 to the 20th power hurts. Would characterize our gamma rays here. And so we can say that our gamma rays are highest in energy as well. And so for part one of our ranking, we would go ahead and label our gamma rays as ranking number for due to the fact that they would occur at the highest energy. And so moving on to the next type of wave that is highest in energy proceed um before our gamma rays. And according to our spectrum that is going to be our X rays here. Again, our X rays occur at a frequency of around 10 to the 20th. Power hurts. And so we can agree that because frequency is related to energy, we have these x rays waves occurring at a very high energy value because of their high frequency and so they are creating these small short waves. So we can go ahead and list x rays third in our ranking because they are second um the second highest in energy now. Moving on before x rays, we're going to continue on and we're going to hit our visible light waves according to our ranking. And this would then be occurring at 10 to the 15th power hertz, which again is a pretty high energy value, but a lot much lower in energy in comparison to x rays and gamma rays. And so we're going to go ahead and label visible light with the ranking of number two because they are the second least highest in energy. And that leaves us with microwaves ranking as number one as the lowest in energy. And we can clearly see that on our spectrum because they only occur at around 10 to the 12th power hertz, which is much shorter than what we found for visible light as well as for x rays and gamma rays. And so we can go ahead and based on our answer choices, we want to go with the answer choice that lists microwaves first because our ranking should begin with the lowest waves that are lowest in energy. So we can already rule out a B and C. And that leaves us with D to consider as the most correct answer. So let's go ahead and begin with part two because we can definitely agree that microwaves are the lowest in energy and gamma rays, we concluded our highest in energy ranking at number four. So part two is concerned with ranking our waves from higher to lower frequency. So this would essentially just be our ranking for part a of our answer, flipped the backwards way. So what we would have is ranking gamma rays as highest in frequency. And that is agreeable because on our electromagnetic spectrum we agreed that any waves that occur past 10 to the 20th power hurts as their frequency will be gamma rays. And so those would be the highest um frequency value. So gamma rays definitely would rank as # one when it comes to frequency. Next, we want to go ahead and and I'll actually put like the frequency symbol here. So we know that that's that ranking. So next we want to go ahead and confirm that microwaves as far as our answer. Nd is the lowest in frequency And based on the frequency value for microwaves, we see that it's occurring at 10 to the 12th power hertz, which is a lot smaller than 10 to the 20th power hurts and anything past it. And so we would agree that microwaves definitely occur at the lowest frequency in comparison to visible light x rays and gamma rays which occur at a lot higher valued frequencies. So we can go ahead and confirm that microwaves would be listed fourth on our ranking when it is in regard to frequency. So we can definitely agree that choice D. Is the most correct answer to complete this example, based on the rankings for part A and B. Of this question. So I hope that everything be reviewed was clear. If you have any questions, please leave them down below, and I will see everyone in the next practice video.