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Problem 9 Medium Difficulty

(a) Find the speed an alpha particle requires to come within $3.2 \times 10^{-14} \mathrm{m}$ of a gold nucleus. (b) Find the energy of the alpha particle in MeV.

Answer

a. $1.9 \times 10^{7} \mathrm{m} / \mathrm{s}$
b. $7.1 \mathrm{MeV}$

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Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

Marshall S.

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Aspen F.

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Video Transcript

for number nine. We want to know how fast an Alfa particle has to be going to get this close to a gold nucleus. Um, so this is moving. We won't know what velocity. So this is the alpha particle. And alpha particle has two protons. This is the gold, and gold has 79 protons atop numbers. Um, so basically, this kinetic energy turns into potential energy. These both positives, like they can republic each other. Let's say it gets to this distance, though. Um, syndrome conservation of energy. Really? So the kinetic energy is equal to the electrical potential energy. You're just gonna do the equation? It's okay. The charge of the one object charge of the other objects divided by their distance. So just gonna plug in my values one here, the mass of the Alfa particle. So that's two protons and two neutrons. So it's four nucleotides, so four times 1.66 times 10th of negative 27. It's my mass, um, terms of e squared. And this is the VM solving for Over here. Kay, that's a constant 8.99 times. 10 to the ninth. The charge is one object. What should the doubtful particle. So that's basically to pro towns. Two times, 1.6 times 10. Then they get the 19th cools the other object, which is gold. That has 79 protons. We've got six times too, ***. 19th. And the distance between them is this. 3.2 times 10 the importing. So now you just bring those, divide those and then take a square root and I get my velocity a CZ 1.85 times 10 to the seventh. Don't report be. They ask what is the energy of this in Mega Electron volts, though. So this would turn out to be in jewels. So when I do, when I do this part of the equation, I get it that my energy is 1.13 six times 10 to the negative 12th. Jules, I'm just gonna d'oh check on my conversion here. Um, one mega electron level is the same as 1.60 times. Tim, the negative 13th. Jules. So Jules cancels and I'm left with 7.1 McGee, electron volts

University of Virginia
Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

Marshall S.

University of Washington

Farnaz M.

Other Schools

Aspen F.

University of Sheffield