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Vibrational spectrum of HCI_Iheory Calculate the vibrational amplitude of a H-CI molecule state:the first excited Eround state, andDescribe wona sketches what nerts...

Question

Vibrational spectrum of HCI_Iheory Calculate the vibrational amplitude of a H-CI molecule state:the first excited Eround state, andDescribe wona sketches what nerts t0 be tolc,b) Create symbolic expression for the vibrational amplitude (this would be the first step of calculating numerica value).Almost all crystals have positive coefficient of thernal expansion In other words , they expands when you heat them_Use the inter-atomic potential energy curve explain qualitatively why crystals expand w

Vibrational spectrum of HCI_Iheory Calculate the vibrational amplitude of a H-CI molecule state: the first excited Eround state, and Describe wona sketches what nerts t0 be tolc, b) Create symbolic expression for the vibrational amplitude (this would be the first step of calculating numerica value). Almost all crystals have positive coefficient of thernal expansion In other words , they expands when you heat them_ Use the inter-atomic potential energy curve explain qualitatively why crystals expand with temperature.



Answers

The radiation absorbed by $^{12} \mathrm{C}^{16} \mathrm{O}$ during a vibrational transition occurs at $2168 \mathrm{cm}^{-1}$. (Section 10.5 ) (a) Caiculate the ground state vibrational energy in $\mathrm{kJmol}^{-1}$ (b) What is the ratio of the number of molecules in the first vibrational excited state $(\mathrm{v}=1)$ compared with the ground state $(\mathrm{v}=0)$ at $298 \mathrm{K} ?$ (c) Calculate the force constant of the bond, assuming $^{12} \mathrm{C}^{16} \mathrm{O}$ behaves as a simple harmonic oscillator. (d) Estimate the change in the position of the peak if $^{12} \mathrm{C}$ was replaced by $^{13} \mathrm{C}$

So we're continuing with quantum chemistry. We have the following equation to consider what looked at it before. So we should already be well practiced with the swear K is the force constant mute is the reduced maths. So what we do, we stop in our values while we're determining k the force constant and necessary instance. So the force constant for 35 c l two is 3 to 3.6 nine Newtons per meter to the minus one. Then we're taking a look at 39 k 35 seat out that is 85.9 to Newtons per meter to the minus one Force constant finally age too. We do not it as five 71.19 Newton's permitted to the minus one. They were taking a look at a second isotope 37 cm off chlorine. We looked at the Saudi five, now looking at the slightly heavier 37 that has an increased value of 552.23

For given that the equation to find the energy of the molecule is energy is equal to end plus 1/2 times H A V, and we should know now that the lowest energy level is when n equals one. So now we have enough information to find the energy we'll get you soap. One is equal to one plus 1/2 because, remember, end is one. Multiply this by Plank's constant 6.626 times, 10 to the negative 34th jewels. Time seconds. And then we multiply that by the frequency that were given 8.85 times 10 to the 13th inverse seconds, and we'll get that piece of one. Or energy is equipment to to 3/2 times 58.64 times 10 to the negative 21st jewels, and we'll get that. Our energy is 87.96 times 10 to the negative 21st jewels. And now we know that the minimum energy that's needed to excite a vibration in seal and that's about 8.8 times 10 to the negative 21st and jewels. And now we also know the equation for the energy of a photon, but if we re arranged it, we confined wavelength. Renta. We know that the wave length Lambda is equivalent HC over e were ages. Plank's constant C is the speed of light, and e is the energy of a photon. So we'll get that Lambda is equal to Plank's constant times, the speed of light divided by the energy we just calculated. And we'll get that land. Our wavelength is equal 2.2 to 6 times 10 to the negative 50 meters. But if we convert this into nano meters from remember we normally describe wavelength in nanometers. We'll get that. The wavelength of excitation is 2260 in nanometers.

So this problem gives us the following equation e n equals and plus one half time's a tch knew which is The new is the frequency, and this is to find the energy off one of these molecules. And so we know that these molecules are in the ground state, therefore, an equals one. And h, of course, is planks constant six point six, two, six times ten to the minus thirty fourth. And the frequency here is given to us as eight point eight. Five times ten to the thirteenth hurts. So this will give us that our energy is equal to eight point seven nine six times ten to the minus twentieth Jules. And so now that we have that energy, we can use the relation e equals H c over Lambda to find the wavelength, which is Lambda. So we rearrange this equation to solve for Lambda we get h C over e. And so now we can plug in our values. Ages, planks! Constant six point six two six times ten to the minus thirty fourth C is the speed of light two point nine nine times ten to the eighth and E is our energy which we just found in the previous step to be eight point seven nine, six times ten to the minus twentieth. And so we can solve this to find that our wavelength is two point two five times ten to the minus sixty meters, and that's our final answer.

In this question, we want to determine the energy and the oil glands associated with exciting. It's cl so the excitation that we're going to be using is we're moving from N. Is equal to one. The quantum number Of N is quote one. And we are moving to end is equality too. So for the energy change, we are going to calculate the energy it Level two and energy at Live one. And then we calculate the difference. And after we have the difference, this is going to be our delta. And we can then use the expression Hc. Over there, we have learned to determine an hour we have. So this is the approach that we're going to be using. Now moving on the one is equal to remember our E. Is equal to end blood half, multiplied by our actions. So what we're going to have here, our e. one is equal to and is equal to one. one plus a half. Multiplied by plank's constant Which is 6.626 times 10. To the power negative 34 multiplied by 8.85 times 10 to the power one drink. So everyone here is going to be equal to 8.8 times 10 to the power negative to zero. And this isn't a joke. Doing the same thing for you to this is going to be equal to two. Plans have Multiplied by 6.6 26 times 10. To the power negative 34. And this will multiply by 8.85 times 10 to the power one drink. So it to this is going to be equal to 1.4 66 times 10 to the Power -1. And this is Joe. Now to determine our joe Trippi this is going to be equal to for example, delta A From one up to two. This is going to be equal to the final energy minus the initial energy. And in this case the final energy is going to be E two and the initial is going to be the one. So our daughter is going to be equal to be 1.466 times 10 to the -1 night My nurse our anyone, we should calculate it to be 8.8 8.8 times standard for negative to zero. So our daughter, This is going to be equal to 5.9 times 10 to the power negative to their enthusiasm jobs. So this is the energy. And then to calculate the wavelength. Remember we're using the formula with blanks constant and the speed of light. So there we have learned This is going to be equal to 6.6 To six which is Planck's constant. Multiplied by the speed of light. three times 10 to the power eight Divided by the Delta energy that we cooperated here. Changing energy which is 5.9 5.9 times 10 to the power negative to zero. So the way of land is going to be equal to 3.4, transplant to the power -6. And this is in metal, and you can convert this into nanometers to say example, this is 33, 90 and.


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