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What type of radiation (in wavelengths, $lambda$ ) would be minimally required to initiate the radical chlorination of methane? [Hint: The initiation step requires ...

Question

What type of radiation (in wavelengths, $lambda$ ) would be minimally required to initiate the radical chlorination of methane? [Hint: The initiation step requires the breaking of the Cl-Cl bond (see Section 3-4).]

What type of radiation (in wavelengths, $lambda$ ) would be minimally required to initiate the radical chlorination of methane? [Hint: The initiation step requires the breaking of the Cl-Cl bond (see Section 3-4).]



Answers

Ultraviolet radiation and radiation of shorter wavelengths can damage biological molecules because they carry enough energy to break bonds within the molecules. A typical carbon carbon bond requires
348 kj/mol to break. What is the longest wavelength of radiation with enough energy to break carbon carbon bonds?

So hydrogen atoms start in the end equal to one state or the ground state. Now using equation twenty seven point one zero on equals twenty seven point one five b. We didn't lie in the state to reach the atom is excited when it absolves the fort on off energy. Twelve points and five second bolt Now a car Using the story questions, we find that Delta e Cuarto and Linus anyone but Ian is the state energy off the state to which the atom is excited after observing the food on on the one is the ground state energy. No, you know that he and physical too negative. Thirteen point six electron gold over and square on. We have there's that as the kind of big energy off the fruit on it is twelve point seven five stronghold. Now we use this a question on also e one iss and get their thirteen point six electron volts. So we used these values and plug them into this equation to find the value ofthe end or the stage to which that is excited so and will then be equal toe negative hurting point six electron volts. Oh, Raj hee won. It's just right expression. First, anyone last El on that on e one isthe negative starting on six electron voice and I was twelve point seven five electron for so we solve it for n Andi Rickard. This valued toe before. So we know that the electron can be excited Who? As high as the fourth level, all the angles to fall on it Now, starting with the electron in the n equals two, four, our bed, the following transitions are possible. So one is and equal to four. Tow n equals two three and equals two. Four. Tow n equals to two and it goes to forward and Nicholas to one. And we haven't equals to treat you any cause to do you can. Also having requested three clinical struan on lastly and first toe tow n equals to one. Now we use a question. Let's move it down a little bit. Not perfect. Now we use the question twenty seven one one six toe. Calculate all the possible Rivlin's that can be emitted as the electron gas kids back to the ground state. Now, according to this question God, you can also use the question twenty seven point nine. That is much simpler. Let's just use that now. According to this equation, one over Lambda is equipped Hard times one over the final state. It's called this an F scared Linus. The initial state an ice crack there are is equal to this and we got this value from example twenty seven point one four. Now the calculations are pretty isn't pulled So let's not we start. I'm during each of this. So for this case and if we are in final is three and initial and his four So we used the value we have to find Landa and we get the value ofthe Landa There will be we could tow eighteen seventy five man emitter similarly for this case and F A stool and and I iss force. So we do the same for each of this case Each of these transition case So we get for the scarce Landrieu's four eight. This explained to Nanami, who are you? This case we have land I call to ninety seven point between you and me. Yeah, we have Landa six fifty six point CNN on Lido Yeah, one zero two point six nine millimeter on the last one we have land goes to one twenty one point five. So these other England's off all possible transitions that they left it can have by cascading tow the ground state.

Let's remind ourselves of a barium court equation equation that we're going to be using. And thats in this equation e equals H C over Lambda, where age is Plank's constant. C is the speed of light and Lambda is our wavelength. However, we want to find just the wave link. So we're gonna rearrange this equation to find Lambda by itself. And when we do that, we'll get that Lambda equals H C. Divided by energy. Our first step is to find the energy perf Otan, so we'll take the energy we were given. 348. Kill it, Jules Promote. Multiply that by in every one mall. There's over God Rose number of photons and we will get there are 5.78 times 10 to the native, 22nd kill a Jules per photons. And now we can plug everything into our Rick Weijden in while doing a little bit of dimensional analysis. We'll get that Lambda equals Plank's constant 6.626 times, 10 to the negative, 34th Jewell seconds times the speed of light 3.0 times 10 to the eighth meters per second. We're going to divide that by our energy 5.78 times, 10 to the negative. 27 22nd Killer jewels multiply that by the fact that in everyone kill a jewel there's 1000 jewels. And then in every one meter there's a one times 10 to the ninth and Nana leaders, and you will get that our wavelength lambda is 344 nanometers.

So now we'LL work on problem thirty from chapter six. In this problem, it tells us that the energy from radiation can be used to cause the rupture of chemical bonds. A minimum energy of two hundred forty three killa jewels for mold is required to break the chlorine, chlorine bond and seal, too. What is the longest wavelength of radiation that possesses the necessary energy to break the bond? And what type of electromagnetic radiation is this? Yeah, so we're told that the energy required is two hundred forty two villages normal. So first thing we need to do is to switch from mole to per molecule so we can convert from most molecules by using our God dress number. So the value which were given is two hundred forty two. Kill Jules, her mole, And then we can move about by Pavel God. Ra's number, which tells us that one mall ah, corresponds to six point zero two, two times ten to the twenty third molecules. So this here gives us for point zero two times ten to the negative twenty two killers, Jules per molecule. But since it's pra molecule, just leave as kill it. Jules and then if we convert to Jules, we just need to move the decimal place over three times. So four point zero two times ten to the minus nineteen. Jules. So this is the energy required to break a CEO bond the CLC. A bond for one molecule. And so we can convert this energy toe wavelength by using our He is equal to H C over Lambda formula. So we have e equals h see or lambda. We can rearrange this equation To be lambda is equal to H C over e and so we need to just multiply clinks constant six point six to six times ten to the minus thirty four times the speed of play and then divide by the energy which we just calculated, which is four point zero two times ten to the minus nineteen. And when we do this, we get four point nine four times ten to the minus seven meters or four hundred and ninety four nano meters. And it asked us what kind of radiation this is. So we can say that this is visible light because it's in the visible spectrum and if we want to be more specific, it's in the blue region of light

I will work on problem one of six from Chapter six. In this problem, we're told about the stratospheric ozone layer help helps to protect us from harmful ultraviolet radiation. It does so by absorbing ultraviolet light and falling apart into a notre molecule and an oxygen atom, a process known as photo dissociation. So you want to use the data and appendix E to calculate the total change for this reaction. So let's go ahead and start their We can write down our equation here for this reaction is oh, three associates to form O two guess and oh, gas. So from the expanding sea we can get the Delta h of information. So if hero to gas is going to be zero because that's the elements natural state for oh, gas, it'LL be two forty seven point five, and for all three, it will be one forty two point three. So Delta h of a reaction is going to be equal to the products minus the reactant. So we go to forty seven point five minus one. Forty two point three gives us a value of one hundred five point two killer Jules Ramon, the next part of this question asks us. What is the maximum wife length of photons can have? It is to possess sufficient energy to cause this dissociation. So we need to convert this one of five point to kill Jews promote to wave one. And what we need to do first is to change from collisions per mole to kill two jewels per molecule. Three. So we write one of five point two kill Oh, Jules, per mole times one thousand first to convert to Jules, then times one over have a god Ra's number to convert the molecules. And this gives us the value of one point seven five times ten to the native nineteen Jules, her molecules. So if we find the wavelength of this light we can do, we can do that simply by using the expression Lambda as equal to H C. Over he where energy is this value and we get a value here of eleven one point one four times ten to the minus six meters or eleven. Forty one thousand one hundred forty nano meters wishes in for a red light


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