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(Hz) is a diatomic molecule Thc two nonradioactive isotopes of hydrogen points) Hydrogen natural abundance, respectively Which molecule is most are H and D with ~99...

Question

(Hz) is a diatomic molecule Thc two nonradioactive isotopes of hydrogen points) Hydrogen natural abundance, respectively Which molecule is most are H and D with ~99.99 and ~0.01 likely to be found in nature?Hz HD Dz

(Hz) is a diatomic molecule Thc two nonradioactive isotopes of hydrogen points) Hydrogen natural abundance, respectively Which molecule is most are H and D with ~99.99 and ~0.01 likely to be found in nature? Hz HD Dz



Answers

A diatomic molecule behaves like a quantum harmonic oscillator with the force constant $12.0 \mathrm{N} / \mathrm{m}$ and mass $5.60 \times 10^{-26} \mathrm{kg}$. (a) What is the wavelength of the emitted photon when the molecule makes the transition from the third excited state to the second excited state? (b) Find the ground state energy of vibrations for this diatomic molecule.

Okay, So in the first part of this problem, really, we must calculate the vibrational frequencies off. The more a coup. Okay, So since these molecules can be modelled toe Ah, simple or morning close to later. We must remember that the vibrational the vibrational frequents off a simple of a simple morning postulator can be found by omega equals que divided by m in this choir grits, we have k, we have em. Therefore, the solution for the first part is going to be one point 13 time Stan Cubic. Divided by 1.725 times 10 to the power of minus 27. The square route. And if we calculate this, we're finding that the the frequency of the air morning pursue later is just eight point 23 times 10 2014. Okay, that's dancer for Bart. Eight now in part B in part B. We're want to find what is the energy and the wave. Elin's off the immediate 14 when this molecule makes a transition between two consecutive energy states. Well, just remember the last question we just saw that the our Morning council later has a quanta off energy between consecutive states That means that the energy of transition between two consecutive states in their morning cosa later is described by H. Omega. So since we want the energy and the frequents off this transition off the photo, this is going to be equal. Let's see, uh, the energy is easy is way. We just have the if recurrence. So energy off the transition is going to be six point 5 82 times 10 to the miners 16 which is the blunt content in electoral votes. Ah, multiply by the frequents, which is eight point 23 times 10 to the 14. Therefore, the energy off the photon emitted is just zero point 4 42 5 42 electoral votes. Okay, well, we just have the energy. Now we have to find a wave of Remember that these a regression the coral they're relates the energy with the rave land for a photo which is e equals h c, divided by lumber. Them therefore la vida, which is what we want. It's just a judge c divided by the energy In the situation. The wavelength is going to be 12 40 just eight c divided by the energy, the energy ISS, you know 0.5 42 and the Waveland Fortis Fortnum is precisely 2 to 90 nano meters. No, no meters. Okay, Dusty Waveland off the photo. Immediate nasty Final answer Control.

Hi everyone. So in this question they asked, Chlorine has two naturally occurring I sort of 35 chlorine abundance 76 and 37 chlorine awareness. 24 of doctors a die atomic molecules in a mass spectrum Pixar scene. For the molecules and for separate for items. How many Pixar in the mass spectrum? So I'm sorry. There are for you pigs in the mass spectrum. Moss spectrum. First week, yeah, for 35 chlorine, then second pig. Big for 37 chlorine, then third pig for yeah, 35 chlorine, 35 chlorine. The um 4th pig. Okay, yeah, yeah. 35 chlorine. 37 chlorine. Then fit big, big. Mhm. Right. 37 chlorine. Yeah. 37 glory. No bits. Barbie. Mhm. First Yeah. Mm. Everybody said at a show of habeas particle. Mm Yeste particle is equal to 74 second. Um Might set a shop lightest particle. Uh huh. My best part of piccolo is equality 17

So if this problem we want to find the number of D 20 molecules, 400 milliliters of water and we know that the frequency of deep items or isotopes this point 01% because this deuterium isotope is really rare. And that's what forms the D 20 So we know that that happens only 0.1% of the time. So the first thing that we want to do is want to find the molar mass of water. It's the molar mass of water. We have to hide regions to reach one point. Oh, wait. In an auction, which is 16 point of world, he had those together you get 18.16 grams per mole. So now that we have the molar mass, we can then go from milliliters of water and two molecules 50 to go because we have all that we need. So first we know that we're starting with 400 milliliters of H 20 or just water with the regular hydrogen isotope. And then we also know that because the density of water is one that for every one of the leader of water, there is one gram of water. And then we just convert this two moles of water by dividing by, the more massive we just calculated. And now for the multi more ratio. In other words, what is the ratio between G 20 and water? Well, we know that it only occurs 0.1% of the time. Which means that there are 0.1 mole of diodes D 20 for every 100 moles of H 20 water. Make sure not to confuse point 01% with 10.1 Because that's not the multiple ratio of vacuum Ultima ratio is even smaller than that. And then finally we just multiply this by Overgaard dress number to go from moles two molecules I don't we add all those together and multiple everything you get 1.34 times 10 to 21 molecules off the to That was the final answer

So we're talking about a vibrational frequency here between two hydrogen atoms, right that air vibrating back and forth like that's a spring. And we're told that that frequency is 1.3 times 10 to the 14 hurts and then were asked, What if they were deuterium? Right? And deuterium has twice the mass of hydrogen, and we want to know what will they buy great with. And the key thing is to recognize that omega is proportional toe one over the square root of mass. We're told that the same spring constant between these two, So it's only the mass that we care about. And so if the mass goes up by a factor of two, right then Maiga has to go down right, because it's in the denominator by a square root of two. Right, Because we have this dependence, right? So that means Omega ends up being 1.3 times 10 to the 14 hurts, just divided by the skirt to to never do that. I get 9.2 times 10 to the 13 hurts, right? Lovely case of proportional reason


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