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The decompostliori of hydrogen iodidc on gok 2 surface 2t ISQ "C is zero oidct in HI HIO) ~ Hz(e) %L3(e)IXMIIE Oto cxpctutcut WNi fourd that tho HI conccutrati...

Question

The decompostliori of hydrogen iodidc on gok 2 surface 2t ISQ "C is zero oidct in HI HIO) ~ Hz(e) %L3(e)IXMIIE Oto cxpctutcut WNi fourd that tho HI conccutration droppcd Goui S4M At tha bcgining of thic cxpctitncut " 0.259 Min 2.262*[0' scconds What j the Valuc of thc Te con;tant fot tlic ICacUOn ut thie temperatute? M

The decompostliori of hydrogen iodidc on gok 2 surface 2t ISQ "C is zero oidct in HI HIO) ~ Hz(e) %L3(e) IXMIIE Oto cxpctutcut WNi fourd that tho HI conccutration droppcd Goui S4M At tha bcgining of thic cxpctitncut " 0.259 Min 2.262*[0' scconds What j the Valuc of thc Te con;tant fot tlic ICacUOn ut thie temperatute? M



Answers

(II) For the ground state of hydrogen, what is the value of $(a) \psi,(b)|\psi|^{2},$ and $(c) P_{\mathrm{r}},$ at $r=1.5 \mathrm{r}_{0}$ ?

The only thing we have to do it. So this question you solved that integral. So remember that the ground stately function because I won 00 is a close to this one. Then substituting his resulting thinking roll we get, is it close to four pi to the outside times the integral from zero to infinity off cubed times These squared which is by are zero cubed under e to minors are are zero times true because it's squared and leaving isn't in rolling's over our then d R. It is equal to four pi divided by pi This factor out times dancing grow from zero to infinity off are divided by our zero cute times He minus two times are divided by our zero on descending relatives over the yard. This is very suggestive as we can now use the fallings institution You easy course too Two times our wedding by are zero Then we got do you Is it true? Over are zero the are so the our course to are zero divided by two times Do you? Then they can take her always four times The girl from when are easy question infinity You was also request Infinity are divided by yours. Your cubed is nothing else. Then you divided by two cube times E to minus two times are zero, which is just you. No, we have d R which is our zero divided by troop. Do you putting these factors outside? And this viper off to keep outside have four times are zero divided by true times one divided by eight To kill times they integral from zero to infinity off you to the turd times e to the minors You do you? These equals two are zero over four times the integral from zero to infinity Off you to the cube to the minors. You do you know we stop here for a brief moment Toe Look at some cool result we choose. Let's define a special function. I offer by the integral from zero to infinity, the ex off key to the minors off X These intimate I was very simple to solve these easy course too e to the minors off Iraq's under miners Alfa from zero to infinity, which is he goes to one over Alpha when he played in the execution Infinity, We hav e to the minors off attempt infinity and e to minus infinity is of course, to zero. So we don't have this term. When you plug zero, we have won over my nose Alpha. But this is the next limits. So we have one minus one over Mina's offer, which is one of replace Alfa. Then from one hand, I, Alfa is he goes to offer my nose one but knows that d y l for overly offa by definition is the coast today integral from zero to infinity off the X miners X taking the derivative with respect to all five of dysfunction z my nose off. Thanks. So look the following taking the derivative off Why? I offer resulting an extra term off miners acts here Sorry our integral It's just the third that even to you off I one then all we have to do is derived these results three times and sensitive in our previous situation. So driving Waas we got leeway Off over the Alphas equals to my nose Alpha minus two There are twice we get minus one times my true time. Lofa Commandos! Free that I have you one more time. We got miners one time My news true times minus free times offer The mine was four. Oh, and also forgot something here by the writing three kinds. We will get a next reminder sign on the outside, which is a desire to hear. So what we need is miners The third derivative, the turn derivative is the course too minus six over Alfa. Before then, miners, the third derivative when now face it goes to one is it goes to six Simple six. Then our barn is equals. Two are zero divided by four times six and then we get our bar. Is it close to treat heart zero divided by truth?

Okay, So this problem, we have a hydrogen atom monitor, actually, uh, inside a container cubicle container. And we have to find the ground state energy off the hydrogen molecules. In a part, A and part B, we have toe. Assume that the thermal energy is given by K b. T divided by two and find what is the frontal number that corresponds to this term or energy? Okay, well, let's begin. Refers to a Bartee would have to find a ground state energy. And to find the ground state energy off these molecules inside of box, we know that is going to be just described by I am a square by square blank crossed in square, divided by two times the mess off this morning, Q times their lunch square off the box. Okay, Uh, first of all, what is the length of the box? They're left off. The box is just 0.2 meters. Okay. Its strength is ink. Emitters, are you know, 0.2 meters. Second, what is the ground state? The ground status. When have when we have m equals one? Now, what is the value off the blank? Constant. The black constants is just one point 0 54 57 times 10 to the miners. 34 Joe's seconds. Okay, Uh, the last finger must calculate is the mess. The mess off the molecule. That's a little complicated, but let's just remember that one. Let's do it here. One mall off molecules is equivalent in this particular case of the hydrogen atom are too times because are too atoms of hydrogen in the molecule times. The mess off the atom in the mass of the hydrogen atom is just 1.0 is, you know? Okay, grams or one molecule. Okay. Uh, therefore, if we cut molecules in here, the molecules in here, we're going to find that them more mess. Do Moller mess off the hydrogen atom is going to be one times, uh, 2.0 16 divided by and a Okay, therefore, that means that the Moeller mess the molecular mess started. Not with the molar, miss, but the molecular mess off the hydrogen atom is just three point 35 times 10 to the minus 27 kilograms. Okay, well, since we have all these data here, there's no medical vatis. We can substitute in the equation and we're going to find that the energy in the ground state for this hi Persian bathroom is just one times. Hi. Uh, times the blunt constant, which is 1.0 54 57 time stand to the minus 34 square. Here we have square also divided by took times The mess the mass is going to be Drink point 35 Time standard a minus 27 times their lens from the box, which is your point to square. And after circulating all this, we will find that this value is 4.1 times 10 to the minus 43 jobs off energy. Okay, But actually, this is the final answer. So the answer for the first part of this problem the ground state energy or these hydrogen Monica is going to be 4.1 times tend to the miners 43 jobs. This is the first answer. The answer. Full part eight. Now, in part B, we have to find the quantum number and the current's bones. Oh, the first point with a thermal energy given by its Britain Here. Term or energy given by K B K B D. Divided by two well in this particular case, we know that. Well, this is going to be equal. Uh, the boats, Woodsman Constant. It's one point 38 times 10 to the minus 23. We don't have a temperature. And this problem is 300 Calvi 300 Calvin divided by two. Therefore, this energy here, it's just, uh, 2.7 times 10 to the miners, 21 Joe's. Okay, well, if we compare this an energy here with the energy in the first part of the ground state, the gross stick energy, this is going to be actually not the ground state energy we want to find. What is the what is the excited state that this energy here corresponds? So we have to We have to make that this energy here. 2.7 times, 10 to the minus. Turn 21 be equal to two. M is square by square, age square, divided by two times more. Lechler mess off the hydrogen atoms, the multiplies, the lunch 100 boxes square. Okay, so therefore, the only variable here that we do not know is the Quantum state. Therefore, if we isolate the Toronto number M, we have that end square. It's going to be cool. Two point, you know, seven times 10 to the minus 21 that multiplies two times more That color mess El Square divided by by blunt, constant square. And this is going to be equal. Ah, five point 05 times 10 to the 18. And if we take, If we took the it's quiet courage, we were discovered that the value off an is equal two point 24 times 10. 39. So the energy level that we're correspond to that specific energy is going to be 2.24 times 10 to deny. Okay, that's defined our answer to this problem. Thanks for

So the minimum kinda big energy the gas should have should is the energy required for the transition from n equals to one Tow n equals to two step. So this kind of begin and you should be e one minus two because the energy had n equals to one is higher. So should we even minus where in and sequel toe make a live off tighten one six and a strong boys over and scratch on You used the question No, ninety seven point five feet. I want this expressions now we can solve for this kind of energy. So we have make it thirteen point six electron voice over one square minus negative certain foreign six electron volts. All the boost on Get this value. Sophie. Ten points to elect on work. Also from the equation. Tarting point eight. We have a relation between kind of thick energy and temperatures, which is given by kind of Kennedy's quite a tree over, too. King time. Steve is the boards and constant. Now we can solve for temperature. It's physical too. Two times. Can it be over? Thank you. And this will be quite a few times. Ten point toe Electron board on. We need to convert Teyla, turn void into tools. So my reply, one point six times ten to the minus fainting. Jules Electron Ward. And we have in the denominator three times the balls, man. Constance. So we solve this for temperature, and we get this to be seven point eight times and two are four. Thank you.

In the laboratory, in the LeBeau Day story, as to as is prepared by cash to S is prepared Bye by the action of by the action of dilute dilute. After two years of four. Did you After two years of four on f e s. So according to the options in this problem, Option eight correct answer option. Age, correct answer for this problem.


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