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Einaaaeon SpcctruinLab pdtkc medrolcn IpcciruniHow AUCI ShGIcicacuhydrogen atom whe[electron moves fromWhat [s the Waclength of the quuntum of light released? What ...

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Einaaaeon SpcctruinLab pdtkc medrolcn IpcciruniHow AUCI ShGIcicacuhydrogen atom whe[electron moves fromWhat [s the Waclength of the quuntum of light released? What color will it be?Heliujzn named After Helios; the Gireek name for the Sun; becuuse evidence for its existence WaS obscrved 1N68 by examining the sun " Decuum. Smnce hclium not found on carth until 1895. suppase ubscnen Encu how you Ihey hed fvund a @eW element 18682ProviousGntbaardNextCuloni ,msliealiontInbat

Einaaaeon SpcctruinLab pdt kc medrolcn Ipcciruni How AUCI ShG Icicacu hydrogen atom whe[ electron moves from What [s the Waclength of the quuntum of light released? What color will it be? Heliujzn named After Helios; the Gireek name for the Sun; becuuse evidence for its existence WaS obscrved 1N68 by examining the sun " Decuum. Smnce hclium not found on carth until 1895. suppase ubscnen Encu how you Ihey hed fvund a @eW element 18682 Provious Gntbaard Next Culoni , msliealiont Inbat



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The sun is surrounded by a white circle of gaseous material called the corona, which becomes visible during a total eclipse of the sun. The temperature of the corona is in the millions of degrees Celsius, which is high enough to break up molecules and remove some or all of the electrons from atoms. One way astronomers have been able to estimate the temperature of the corona is by studying the emission lines of ions of certain elements. For example, the emission spectrum of $\mathrm{Fe}^{14+}$ ions has been recorded and analyzed. Knowing that it takes $3.5 \times 10^{4} \mathrm{kJ} / \mathrm{mol}$ to convert $\mathrm{Fe}^{13+}$ to $\mathrm{Fe}^{14+}$ estimate the temperature of the sun's corona. (Hint: The average kinetic energy of one mole of a gas is $\frac{3}{2} R T$.)

Everybody. So many friends. A What is probability of the Adam Be? Um we need to find the seconds and see protons emitted from second buys Solar type star. So from E, we have e equals h c land. Um and that is a plaints. Concepts of 6.63 times 10 to negative 34 Jules per second times. Thus the right times 10 to the eight meters for seconds divided by 21 centimeters which is gonna be times 10 originated two meters and this is gonna equal 9.47 times ton to negative 25 jewels. And I we have temperature equals land a t land a here any 2.98 eight and who's times Times 10 a journey of three m kay divided by 21 times 10 to negative two meters and we get 0.138 Kelvin's And now we could find the probability. So we got probability equals e to negative e k temp. Oh, it's not divided buys. I e get Kate on and by temperature divided by 3.5 times tied to the 14 us. So here we have e and we have the energy which is getting about here at 9.47 times Tach negative 25 jewels times 1.38 times 10 to negative 23 drools by by K. Times 0.138 Que Calvins divided by 3.5 times 10 to the 14 seconds. And this probability, we get 1.77 times 10 to native 17. And now we have B and we have the rate of mission. So the rate of mission rate of mission is gonna be equal. Teoh one full time vita by 3.5 times 10 of the 14 seconds times one adam. And now we need to know the number of protons. So we have number of faux times equals we have the readmission. So one proton divided by 3.5 times 10 to the 14 seconds times one Adam times, six times 10 to the 59 Adams. And this whole thing is gonna be 1.71 times 10 to the 45 full times. If I can spell photons here for everybody, throw times for second and this is the equal signs. Let me like, make that equal sign look nicer. People sign. OK, And as for B now we have C and C. It's just gonna be 1 70 wine times 10 to 45 boat times divided by 1.8 times 10 2 45 pro times. And it's gonna be 0.9. Okay, only 95%.

Okay, Serving Chapter 37 problems 60 it says in the sun, and an ionized human Adam makes a transition from equals five to in calls to state admitting a photon that says, Can that folk can be absorbed by hydrogen atoms Present the sun. If so, between what interview states with the hydrogen atom transition her. Okay, so Singley ionized helium. It's like hydrogen, except that they're too positive. Charges betweens Z equals two in the nucleus in the square of the product of the positive and negative charges appears in energy term for the energy levels so we can use the results for hydrogen. We replace e squared with disease where he squared as we've been before. Probably. So that means using the Bohr model only a e in this e equals negative Z squared now of 13.6 TV over and squared. Cool. So this is a really good way, an easy way for us to really any hydrogen like Adam with a different nucleus with more charges in the nucleus, for example. Okay, so for helium, we said Z equals to hear so spun that issue. We've negative to square turns 13.6 e V over in square. So this is the same as negative 54.4 e v over and square. And that's our e n. Okay, so if we want the energy from in five, it eats too. Don't The E year has just given as you five minus you too? So this is negative. 54 point for E V. Over one over five squared, minus one with two squared. You should see this comes out to being 11 4 TV. Okay, So if that's our energy transition now, it also asks, um, can that boat don't be absorbed by hydrogen atoms? Well, this is not the energy difference between any two specific energy levels for the 100th. Adam, you can look at that if you want to look back at the figure 20 six from the previous problem. If you have a problem 56 you should see that all of the gaps between the energy levels are smaller until the very last one, or they're all get bigger. As you go toe toe, lower energy levels gaps. Right. And the biggest the gap is there can be from in equals. Two equals. One is, um roughly what is that a 10 point to electron walls? Now, if we add another one point nine electron volts that gives us that equals three equals one transition. Now that gets us really close. But I don't think this 11 to electron volts. So then we go. One more energy level past that equals four down two equals one, and that's passed him up. Quit for that crumbles. So if you look back at the energy diagram, this does not match any tradition for the hydrogen Siri's, which means this cannot be absorbed by the hydrogen atoms. So once this helium with its position, this photons will not be absorbed by the hive school.

To find the probability that a given animal make a transition in one second, when, on average, each Adam remains the higher state for 3.5 times 10 to the 14 seconds we find me define the energy in the temperature. This is because the probability P is e to the minus is use concert to the minus C over K B T. Where K B is the bolts been constant, divided by the total time for decay 3.5 times 10 to the 14 seconds The energy here e is equal to H C. Over Lambda H is Planck's Constant C is the speed of light, and lamb does the wave length. This is 21 centimeters, or 21 times 10 to the minus two meters. So plugging in these values, we find that the energy here is equal to 9.47 times 10 to the minus 25 jewels. Oh, we can also find the temperature here using the Wien's Displacement Law, which says that the temperature is equal. Ooh, the constant 2.898 times, 10 to the minus three meter Kelvin, divided by the wavelength again. Lambda is 21 centimeters or 21 times 10 to the minus two meters. So this gives us a value for our temperature. Um, of zero quaint 0138 Kelvin. So it's pretty cold. So playing in this value for our energy and our temperature and the value for the bolts been constant and units of Jewell Per Kelvin, we find that the probability is equal to in one second. The probability is equal to 1.77 times 10 to the minus 17 which is really small and make sense. But it's very small since it has such a long time 11 million years for it to decay. For for Part B. It says there are six times, 10 to the 59 Adams of neutral hydrogen and the cloud. So how many photons are there that are going to be radiated? So one skill here, the number of photons we can call this in gamma is equal to the rate of a mission of a photon. We can call this our times the number of atoms in today over told that the number of atoms is six times 10 to the 59. So what's the rate of a mission, Then, while the rate of the mission is how much we have one photons per second, Adam. So we have one photons. On average, we have want one photo on, and then what's the time? All the time is 3.5 times tended of 14 seconds. And then you get Mrs Times the number of atoms. So the member of photons that we end up with is equal to, um, 1.71 times 10 to the 45 photons per second communities here. Photons per seconds. Let's take that out. Lastly, for part C, where it says how toe, How does this number compared to the 1.8 times 10 45 photons admitted each second by a solar star? To do this, we just simply need to take the ratio. So our ratio is in gamma divided by the that we found in part be divided by the number here which, uh, for the Star, which was 1.8 Tim's tend to the 45. So this comes out to equal 0.95 So from these values to clear the number of photons emitted per second by Ha Jin by the hydrogen cloud of 0.95 times the number of photons emitted by a solar type star.

This question reoccupy under its helium. My own right, actually emits makes a transition from very close to six to get close to, and he meets some fort on. I want to see if this fold one can be absorbed by and the hydrogen ETA. Right? Gonna assume the 108 obesity going state and close to one. Gonna see what energy states can be excited too. So first off, to find what is the energy of discovery, We need to know that the modesty in if your energy levels for here plus so he can pass is 100. I own that. That is, it has only one electron orbiting it. Right? But its nucleus. It's not just one proton. It contains two protons. So in this case, the energy at any level, she goes toe negative. C square time. Sti expression for the hydrogen. You okay? I saw this theater additional Z square here because I was e. It's not cost one like in hydrogen, but rather it goes through to so speed Negative four four to finalise the energy of the armory speakers too. Six minus 82. You can't show 0.1 e v. No looking at the different transitions for our hydrogen hydrogen atom. You can see the acute 0.1 TV actually corresponds to the jump from any Costa 12 and close to treat. Thanks. So this is our transition and therefore the hydrogen atom could be excited from any question, one to any question treat.


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