So what discussion we don't still have. If this expression for the total potential energy to find what is the force that is accepted what I own, the force we know is related to potential energy by negative you d r She did in this case, if you were to differentiate, this gets negative. Help, uh, square off for scrap plus B types em over our tip off and plus one. So this after differentiating no Eddie equal book point, That s where are those? Two are not equal billing point. We expect that the net force acting on the iron must be, uh, zero. Right? So that it is It doesn't move right. So it's in the group. So if you want to find what is unknown, be we can actually get set ethical toe cereal When Archos who are not Yeah, try to We arranged to question a bit electrolysis t exhibition. And if you go to were vicious, find what it's b should be to be so far que e square over m times are not and minus what No, associating just very well be into our expression for F. All right, so now we have two different Ask one are not which is a constant the liberal spacing if our which is to be favorable. So now we can simplify the expression for force a bit from Hugh by opening only broadcasts and organic common terms, which is l far kiey Square. Well, for, uh, Oscar? Sure. Yet one minus. Uh, not over Are to the poet off and minus what? Which is the expression that is given a key question. Right you have to do here is you just had to pull out our square from this. This just r squared times our tip off and minus one, right, So that we can combine these two together. I know it's over our to pull a minus one. No foreign export this question. Ah. Want to you mentioned debts. The story is not displaced by small distance s. So basically be looking. It's are becoming are not plus some small distance s right from the group in point. They want to find what they see force that respecting on it. So this t expression No, since are not So you are. It's no given this, uh, not us. If can actually be Please are not. Yes, uh, minus s. So this would be Come, just focus on this here. Or rather, let me just focus on the, you know, record this. We just ar minus s over our po off a minus one. Just one minus s. Or because this is very, very small. Small, much smaller than our. So we can use the binomial expansion for this undergoing binomial expansion. Take e TEM Just negative s over our I want to buy t pol minus one thus so I don't so far right, but we ignore the higher power terms. We just truncate Eddie. Second took So it's just an approximation course Os my is much less than our. So this term is very, very small. Less than what? So we can't use the binomial expansion putting that back into the expression for force commission, but first becomes negative. Feel far square for Oscar one minus one plus S o. R and minus one. This becomes l far negative. L far, kid, You square off square times. Yes, over our tires and minus one. We have inching this a bit gets But if so far when it's one times this, so we But it's our O s. It's very, very small. So our is actually can be approximated s are not. Of course, this is very, very small. So this is approximately just negative Off k square are not cute times a minus one times Yes, we see that this is kind of flighty coleslaw where this is our spring constant K and SST small displacement. And this K is indeed what is given Indie question might be one k to be this key off e squared about Don't square so they are not cute. Time say much one. So now we're gonna put some theoretical values into this expression to find the figures, your vibrations, vibration we can assume because it is a small displacement, it acts like a simple human emotion. So what if because he just goes to, uh, one over two pi time skirt off k over him. So the K value, as described earlier, is self r K square. Cute him with this one, you had to find ways on what's so from the figure 38 0.2. We actually see that the inter atomic distance between sodium, sodium ions in the Sudan. Correct. Uh, crystal is your 0.56 to 737 centimeters. This between sodium and sodium. But what we calculated the are not we sure is the distance between sodium and chlorine. So approximately we have one chlorine with one saw him. So approximately half way between would be the chlorine UK, right? So we expect the sisters for are not to be about half that's office distance between the sodium ions. So there's approximately 0.2 it one for Said promised night. It does so using this, we can actually calculate Uh, okay, this stiffness constant bringing El Far to be 1.7476 Que is just a point I know Stand up all night elementary, church squid If you are not to point it One step pole off my s name. Cute. So it is 20 times for minus 10. So you should start the decimal point by one. So this understand? Cute. And then we have m minus one where m is eight. So it's minus one. You should get a constant about 1 to 7 insurance per meter. You know, we really find the frequency one of ah pie. Then we have 1 to 7 at the top and we have to mess below I. So far, the mess of the sodium ion is 20 tree atomic mass units. So we've got a competition. 2 kg? No. If they think this, we should get 9.1 its extent off shelf huts.