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Problem 95 Easy Difficulty

In beta decay, a nucleus emits an electron. A 210 Bi (bismuth) nucleus at rest undergoes beta decay to $^{210} \mathrm{Po}$ (polonium). Suppose the emitted electron moves to the right with a
momentum of $5.60 \times 10^{-22} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ . The 210 $\mathrm{Po}$ nucleus, with mass $3.50 \times 10^{-25} \mathrm{kg},$ recoils to the left at a speed of $1.14 \times 10^{-3} \mathrm{m} / \mathrm{s}$ Momentum conservation requires that a second particle, called an antineutrino, must also be emitted. Calculate the magnitude and direction of the momentum of the antineutrino that is emitted in this decay.

Answer

$1.66 \times 10^{-22} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$ to the left

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Video Transcript

{'transcript': "it's a problem. 8.89. This is actually a pretty cool example of just how how powerful the conservation of momentum can be. Because this is how a new type of particle was A new type of elementary particle was discovered in the early 20th century. It was noticed that in May 2 decays, which is where ah, the nucleus of an atom emits an electron and gains a positive charge. And this becomes the nucleus of another element. In this case, we're looking at business to 10 decaying into polonium 2 10 and it was found through experiments that the momentum is not concerned with in this case, this is starting at rest. And the moment, um of the electron is not equal and opposite to the momentum of the polonium nucleus here and, you know, suggested that perhaps of the conservation of momentum isn't always true. But, um, Wolfgang Pauli Actually, it was like, Well, maybe there's this other particle that was getting admitted, and it's hard to detect, and he turns out he was right. It's sort of a bit controversial that controversial because it's like, Well, okay, you say this exists, But where is it just turns out that neutrinos that report anti neutrinos in this case are really hard to detect anyway, getting too the problem itself. We know that the momentum of our polonium nucleus, plus the momentum of our electron plus the momentum of our, um, neutrino. This is the Greek letter new, by the way, anti neutrinos. A bar over it. Uh, this s t equals zero. Now, since these are both moving in the ex direction, there can't be any white component to the mo mentum of the neutrino and the neutrino. Uh, so this is just for the ex components of these. And, um, yeah. So the momentum of our anti neutrino that looks like a let's just call it a neutrino. It doesn't really matter for our purposes is just the negative of the momentum of polonium nucleus, minus momentum of electrons Fairly easy. So we put all of these numbers in, and we find out that we get a negative 1.61 times 10 to the negative 20 seconds. Graham, you choose for a second. So it's moving off to the left so we might know dry our neutrino out here. It should be level with ease. But you know, there's only so much space put a bar over it, since over here, there's enough room and yeah, you can see that actually, the electrons moment of this 5.6 times, 10 to the negative, 22nd commuters per second and this is the same of the same order of magnitude. So there's quite a lot of momentum that's missing from this polonium nucleus you can see says so this was quite a mystery for a while, but then they eventually solved it, and then they eventually found out that the solution, the neutrinos and anti neutrinos also actually exist. So it was a solution that actually works."}