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Review ConstantsWhen displaced from equilibrum by smal amovnt the two hydrogen atoms an Hz molecule are acted restoring lorce F; Kzwith k1 540 N/mPan ACalculate th...

Question

Review ConstantsWhen displaced from equilibrum by smal amovnt the two hydrogen atoms an Hz molecule are acted restoring lorce F; Kzwith k1 540 N/mPan ACalculate the oscillation frequency of the Hz molecule Use meff m/2 as the effective mass" of the system, where mn in the mass of hydrogen atomTake tho mass of hydrogan atom a8 1.008 whora u = 1.661 * 10kg: Exprass your answer In henzView Avallable Hintls)AZdSubmit

Review Constants When displaced from equilibrum by smal amovnt the two hydrogen atoms an Hz molecule are acted restoring lorce F; Kzwith k1 540 N/m Pan A Calculate the oscillation frequency of the Hz molecule Use meff m/2 as the effective mass" of the system, where mn in the mass of hydrogen atom Take tho mass of hydrogan atom a8 1.008 whora u = 1.661 * 10 kg: Exprass your answer In henz View Avallable Hintls) AZd Submit



Answers

When displaced from equilibrium, the two liydrogen atoms in an $\mathrm{H}_{2}$ molecule are acted on by a restoring force $F_{x}=-k x$ with $k=580 \mathrm{N} / \mathrm{m}$ . Calculate the oscillation frequency of the $\mathrm{H}_{2}$ molecule. (Hint: The mass of a hydrogen atom is 1.008 atomic mass units, or 1 u; see Appendix E. As in Example 13.7 (Section $13.4 ),$ use $m / 2$ instead of $m$ in the expression for $f$ )

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.

For but a off the given problem. They loved values off vibrational energy off guy a week. It don't make molecule. Molecule is given by e V is equal to three plus one or two. Um, it should be right by to buy this times the square root off K derided by reduced Mass Where we here is the Web racial, quantum Burke is the force constant off the born in the molecule and a said movies the reduced muscle from what you it is given that the N O molecule observes a fort only the frequency off 56.3 times 10 to the power 12 hurts to make a transition from we use equal to zero to reason equal to one we didn't know change in rotational state. We know that the energy off a four tone with the frequency of the F is given by Jeff is a call to even minus steely. Not then we substitute the energy value from the equation that brought here Excuse us. An expression that he's some defined expression will be HD made by to buy Times Square root off a Katie, right? I knew Then the next step will we solve for a mule. So the expression form you released months we get here is OK. Divided by four by square square arm. Using the care value, there is a 15 30 Newton meter divided by four by square. If we have is a 56.3 times 10 to the power 12 we take the square, we get the reduced muscle for 1.22 times 10 to the power, minus 26 kilograms. Then for the part be off the problem, we can, uh, compute the value off mule. Um, using equation that is questionable or 42.4. Um, this is for part B. Where M and physical to 14.0 70 atomic marsh village. So this is not produced. Mask on. A more serious to you where, uh, Marcelo full his 15.999 atomic machines. Then they reduced. Mars will be Marcel for in Marcel for all derided by Marcel for n plus masterful supplying those values in converting into kilograms, which means multiplying the atomic Marcy entry there 1.66 times Interpol minus 27 k g. You get there this mosque to be 1.24 Dimes Dental baller minus 26 kg for part C off the problem. The results that we obtained in a party, which is this one you, which is one point which is 1.22 times into power minus 26 where we have ah, King part of you. 1.24 I agree they're small. Difference between them is because of the answer tending the data.

So here we're continuing on with the idea of quantum chemistry. So we'll be looking at the relation between the vibrational frequency on the force constant that is represented in the following equation. My case of juice is a force constant music produced mass. So we're given the force constant. We calculate our reduced mass, but is no 0.99 multiplied by 1.66 times 10 to the minus 27. Plug those numbers into our equations. Gonna be not hate guy. That is 2330.1 centimeters to the minus one where we already knew that Kay was 317 So now we're filling in the exact same equation for a different example here. So I calculating a different reduced mass on any second part. Reduced mass is one point 97 times 1.66 times 10 to the minus 27. So then are be not for D I because we're looking at deuterium here, So it's twice as heavy as hydrogen. It's also written was that whereas our first hydrogen is considered by that symbol, so are calculated. Value is 1651 0.74 centimeters to the minus one

Someone way have que prime it waas reduce mass dimes two pi f square of that reduce masses m one m two over m one trust em too. Times to buy f squared. Putting the numbers in You will find k prime to be 963 Newton permitted now J e for and thus one minus and equals and just one thus half minus and thus half times h f it was HF which is independent off.


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