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(a) Triply charged uranium-235 and uranium-238 ions are being separated in a mass spectrometer. The much rarer uranium-235 is used as reactor fuel.) The masses of the ions are $3.90 \times 10^{-25} \mathrm{kg}$ and $3.95 \times 10^{-25} \mathrm{kg},$ respectively, and they travel at $3.00 \times 10^{5} \mathrm{m} / \mathrm{s}$ in a $0.250-\mathrm{T}$ field. What is the separation between their paths when they hit a target after traversing a semicircle? (b) Discuss whether this distance between their paths seems to be big enough to be practical in the separation of uranium-235 from uranium-238.

Part $(a) :$ The separation between the two paths is 0.025 $\mathrm{m}$Part $(\mathrm{b}) :$ The separation between the two paths is 2.5 $\mathrm{cm}$ and this distance is more than enough to differentiate between the two isotopes.

Physics 102 Electricity and Magnetism

Chapter 22

Magnetism

Magnetic Field and Magnetic Forces

Sources of Magnetic field

Electromagnetic Induction

Inductance

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Lectures

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In physics, a magnetic fie…

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Singly charged uranium-238…

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Singly charged uranium- 23…

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Suppose that an ion source…

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A uranium nucleus (mass 23…

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$\bullet$ A singly charged…

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A mass spectrometer is use…

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A proton with mass 1.67 $\…

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A 4.78-MeV alpha particle …

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A $4.78-\mathrm{MeV}$ alph…

05:34

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A particle passes through …

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A mass spectrometer has a …

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Consider the deuterium–tri…

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Protons are projected with…

So you're in you. I said apps are being separated, but you must speak. Told me to So the hell juri noon 200 Uh 35 you're earning 238 And one off them is where and this one is used as a fewer in a reactor. So we need to separate them and get these useful isotope separately. So they held masses, which is giving three. If you put your name and sue for 3.95 10 minus 25 keep the grooms and we know that my field pick told me to He is 0.20 fire, you person and the velocity off each visitor bees So eating in feat fifth power meters per second. So imagine we have a team off these mixture off user tips and we want to separate them knowing that they have different masses, we can guess that they would have different trajectories in the magnetic field. So while they are charged and we know that it is said that their tree plea charged, that means they have, uh, three times gather to charge. And after they make a how have Sukru they're taking my respect emitter and we need to find a difference. Deters between the ropes after half circle. So let's write down O R formula So Lauren's force for on generally for ah charged particles Q will be, and this is equal to him. We squared over R and we can rewrite this as two. And we squared over tea where these at the emitter diameter. So you free sing, please. Abstract is diameters. We will get our desired result. So let's just can So one would be here and we will have de ese too. And we over q B and difference between these diameters would be D one minus Tito, which would be to be they were a kid Q B name, one minor, same being in two and no did these difference. He's a difference in must. We can conquer all Khalkhali eat, and it is 0.5 10 minus 25 kilograms. But ah, it is useful to check, uh, in another way. So with the difference between these isotopes eso this number tells us how many ah nuclear particles are there into nuclear's. So this tells us that uranium toe 38 his three more new nutrients, then you're immune to 35. So this mass difference should be three times nutrients mass. So it is useful to check that this is true. You can search. What is the mass off a new throne end If Aah! These data is in Correspond this or not so But from here we have everything and we can calculate the difference. And we also know what is the, well, a city. We also know what is the magnetic field and Q, as I mentioned Ah, it is Tripoli charged. That means the cue. The charges three times elected charge, which would be three multi one points. Extend minus 19. Cool. And the result becomes 2.5 centimeters. And then, um if it is, If this gap is large enough, toe actually separate this. Ah, irons. And the answer is yes, of course. Uh, these cops would be he knows toe separate. This Ryan's

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