(II) An atomic nucleus initially moving at 420 m / s emits an alpha particle in the direction of

Name: Problem 14, Chapter 9: Physics for Scientists and Engineers with Modern Physics
Uploaded: 2019-06-27T00:04:58-08:00
Duration: 1 min 53 s
Channel: Farhanul Hasan
Description: (II) An atomic nucleus initially moving at 420 m / s emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350 m / s . If the alpha particle has a mass of 4.0 u and the original nucleus has a mass of 222 u, what speed does the alpha particle have when it is emitted?

step 1 Okay, so momentum conservation requires that initial momentum will be equal to final momentum. O

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(II) An atomic nucleus initially moving at 420 $\mathrm{m} / \mathrm{s}$ emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350 $\mathrm{m} / \mathrm{s}$ . If the alpha particle has a mass of 4.0 $\mathrm{u}$ and the original nucleus has a mass of $222 \mathrm{u},$ what speed does the alpha particle have when it is emitted?

   (II) An atomic nucleus initially moving at 420 $\mathrm{m} / \mathrm{s}$ emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350 $\mathrm{m} / \mathrm{s}$ . If the alpha particle has a mass of 4.0 $\mathrm{u}$ and the original nucleus has a mass of $222 \mathrm{u},$ what speed does the alpha particle have when it is emitted?

Physics for Scientists and Engineers with Modern Physics

Douglas C. Giancoli 4th Edition

Chapter 9, Problem 14

Instant Answer

Solved by Expert Farhanul Hasan

06/27/2019

Step 1

According to this law, the initial momentum of the system (before the emission of the alpha particle) is equal to the final momentum of the system (after the emission of the alpha particle). Mathematically, this can be written as: \[m_{i}v_{i} = m_{f}v_{f} + Show more…

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(II) An atomic nucleus initially moving at 420 $\mathrm{m} / \mathrm{s}$ emits an alpha particle in the direction of its velocity, and the remaining nucleus slows to 350 $\mathrm{m} / \mathrm{s}$ . If the alpha particle has a mass of 4.0 $\mathrm{u}$ and the original nucleus has a mass of $222 \mathrm{u},$ what speed does the alpha particle have when it is emitted?

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Key Concepts

Recoil in Particle Emission

When a body emits a particle, conservation of linear momentum results in a recoil effect, meaning the emitting body must move in a manner that balances the momentum carried away by the emitted particle. This concept is important in nuclear reactions or decay processes, as it relates the velocities and masses of the resulting fragments, enabling the calculation of the emitted particle's speed based on the known mass and velocity changes of the residual nucleus.

Conservation of Linear Momentum

In any isolated system, the total linear momentum remains constant, regardless of the interactions between objects. This principle is fundamental in analyzing processes such as particle emissions or collisions, where the momentum before the event must equal the momentum after the event, allowing for the determination of unknown velocity components if the masses and remaining velocities are known.

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