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Between Carbon andhydrogen 5.s lormt mathane chotnhct Ict Ine e4diorKmaltcortect nxrEsslon Ir tha e quilbiu culelantC()+2H (g) CH, (g)Ke = ICI |R =Rc = [HakIc ua]&q...

Question

Between Carbon andhydrogen 5.s lormt mathane chotnhct Ict Ine e4diorKmaltcortect nxrEsslon Ir tha e quilbiu culelantC()+2H (g) CH, (g)Ke = ICI |R =Rc = [HakIc ua]"

between Carbon andhydrogen 5.s lormt mathane chotnhct Ict Ine e4dior Kmalt cortect nxrEsslon Ir tha e quilbiu culelant C()+2H (g) CH, (g) Ke = ICI | R = Rc = [Hak Ic ua]"



Answers

The three lowest energy levels for atomic carbon (C) have the following energies and\ degeneracies: $$\begin{array}{ccc} \text { Level }(\boldsymbol{n}) & \text { Energy }\left(\mathbf{c m}^{-1}\right) & \text {Degeneracy } \\ \hline 0 & 0 & 1 \\ 1 & 16.4 & 3 \\ 2 & 43.5 & 5 \end{array}$$ What is the contribution to the average molar energy from the electronic degrees of freedom for $C$ when $T=100 .$ K?

Hello. All right. And this question we're asked to calculate what energy state a central carbon atom is in a white dwarf where the temperature is around tentative for Calvin's. And were told to use the approximation that the energy off the atom, the kinetic energy of the atoms. So the energy associated with the vibrations is 3.5 times the Baltimore constant times of temperature and cap. It's We're also told that we can kind of assume the carbon atoms to be forming a lettuce where the spacing between the letters points is about 20 cm. So we're told to approximate the colon potentials coming from the neighboring atoms. Um, if you consider three atoms to be uh that of a quadratic form. So the way we do this is we look at what the potential for a point charges. So that's what one of the nuclear is going to represent. And it looks kind of like this. So it's me R. Is equal to K, times Q. Coolness, constant times the charge itself divided by the distance to the point of interest from the church. So if we can add up the potential is coming from both neighboring atoms of a central atom and it's going to be K. Times cube times and brackets one over a minus X plus one over a plus X. Right. We assume that X is a small vibration around the actual um kind of locked position of where the central atom should be. So it kind of oscillates or vibrates a little bit away from it. So if it does so then this is the potential that we get and we're going to try and massage this into a quadratic form. We're told to approximate this into as a quadratic such the X. Is small. So we're going to look at a combination of 1/8 plus X plus 1/8 minus six. So since we know that a A is much greater than excesses, the vibrations are small. We can factories one over a from both fractions and we end up with 1/8 times in brackets 1/1 plus X array plus 1/1 minus x away. And then we can use the expansion that one minus X where X is small, small number to the minus one. This is approximately one plus X plus X squared plus that of the right. So higher order terms, terms of order X cubed and higher. So we used this approximation to expand both of these fractions and then we look at what happens. We suffice with going to quadratic terms. That's the first non vanishing term after the constant. So here we have 1/8 times. Uh in brackets one minus x ray, plus x squared over a squared plus. Then we kind of the cubic terms from the first expansion. Then we move on to the next expansion which gives us one plus X over a plus X squared over a squared plus the cubic terms from from the second expansion. So if you look at it ordered by order, the first term, which is the zero order term in X doubles up. Then we see that the at the first order. So linear ordering X, the terms cancel. And then finally the terms in quadratic order in X. So second order an X also add up. So everything doubles up. That is of even powers of X. So we can factories to an approximate this. Um won over a a plus X plus one of our uh minus X uh function as to over eight times one plus X squared over a squared plus. Of course, cubic order, potentially cubic order terms. Okay, that's the approximation. And so the potential itself looks like two times KQ over a times one plus X squared over a squared or expanding this out of course is two times KQ over a plus two K Q over a cubed X squared. Now it's important to emphasize that this is the potential. It's not the potential energy. We're going to look at the potential energy. Right? So the potential energy is going to be E. P. Is equal to Q times the potential. So the charge times the potential and this is equal to two times K times K times big. Few times they look you over a plus, two times K times big. Q times to look you over a cube of big and little cues are the charges of the carbon atoms. So it's going to be the same positive charge for both of them. And here I just assumed that it was singly charged positive carbon iron, but you don't have to do that. You can assume that there is all four um uh, charges on the carbon atom if you want. Um So the point is that the second term that we get here is two times K times Q squared over a cube times X squared. So in terms of our potential energy interpretation, this bubble factor is half m. Omega squared, omega is going to be the energy that we are interested in. So it's gonna be the energy associated with the vibrations. And so we can rearrange that to find what omega is. So we say that a half and omega squared is equal to is equal to two times K, 10-K times Q squared over a cube in rearranging that for omega we get that is equal to the square root of four times K. Times he squared over Emma cube. Now we can multiply this by H bar and if you multiply it by H four then we actually get the spacing between the energy levels and the harmonic oscillator. Remember that the harmonic oscillator energy looks like this. So we have um and plus a half times H bar omega. So if we know mega multiplied by H bar, then we get the spacing in the energy levels and this works out to be 8.0, attempted to minus 15 jewels. If you put in all the all the numbers that you provided, so and we have this and then we're going to um multiply or we're going to calculate the energy associated with these vibrations coming from the temperature. So that energy is what we're told to use. So that energy will be this formula over here, the three halves K B. T. Which is just the energy measured in the degrees of freedom that the particles have. So if they're kind of just y breeding around, then this is part of their kinetic energy. So what we would have to look at is um you know, if they are logged into into into place, then they don't actually have too much of a kinetic energy themselves, like actually translation of kinetic energy. They have vibrational energies instead. So this energy is what is going to be made up of the vibrational modes. So we have to evacuate these two to each other. Okay, so these two energies, the oscillator energy is going to have to equal the thermal energy and we can rearrange this for end and we're going to find that end is approximately minus a half. Okay, now, what this means is that and is actually zero. Okay, so an is actually zero. And the energy left in this approximation for the energy levels, or this approximation for the thermal energy of the atoms is not enough to actually excite any of the vibrational modes of the, of the harmonic oscillator that we model this way.

Explanation for the given problem? Yeah problem. 39 there is the c eggs C. X. Found energy order for carbon trail light is here we have Born energy um here we have an option C behave carbon traveler right is greater than carbon tetrachloride. Then carbon etcetera, bromide and then um chlorine. Carbon tetra I date carbon cetera today. So this is here um you know did here chlorine is more electronica. Tiv has high electronic nativity and like draw neG activity. DVD and Lorena's mood electronic activity and his small size small in size and must have strong strong bound. So don't the group here don't group it is degrees. We can say that C. X. Born energy order of carbon to trap highlight is decreased on the group because don't the group electro negativity decrease in size, bone land will increase. So here correct option is option C. CFO carbon traveler right has greater mount energy than carbon tetrachloride than carbon trouble might then carbon tetrachloride. So Cst correct option

Hi in this problem We are given four structures as A B, C and D. In which one carbon atom is underlined. We have to identify the structure where the underlying carbon atom is sp three hybridized for this river. Right? The complete structures for the compound You can write for this CH three C. H double born. See bitch, bitch. The second structure is CH three, C HH Single one Ch 3. The C option is CH three C double born, oh, C H three. And the the option is CH three CH two, C triple born. And now a carbon which is all the full single bonds is sp three advertised as you can see in all the food structures the structure B has a carbon that is underlying and it is sp three hybridized carbon atom. So the option B is that correct answer? That is the underlying carbon is sp three hybridized in that compound. Given an option B. That is see it's three C H two C H three

The question is correct order regarding the electron negative of electronic nativity of hybrid orbital off carbon is so correct. Order regarding regarding electronic nativity, elect through negativity, activity of I breed are vital. I breed are vital of carbon is Sp is greater than sp two Is Greater Than Sp three. Sp. Hybridized carbon is most electronic active, and sP three is sp three. Hybridized, carbon is least electronic active. This is most electronic active, This is least electronic active. So now let's take out the options. It's accord the options. So we see that of sunday's correct.


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