Explanation Given info: The mass of alpha particle is 4 m p and charge is 2 e and radius of proton trajectory is R . The given diagram is shown below. Figure (1) The formula to calculate the magnetic force acting on an alpha particle is, F α = q α v α B α (1) Here, q α is the charge of the alpha particle. v α is the velocity of the alpha particle. B → is the magnetic field. The centripetal force acting on a alpha particle of mass m α is, F = m α v α 2 r α (2) Here, m α is the mass of alpha particle. v α is the velocity of the alpha particle. r α is the radius of the trajectory of alpha particle. Equating the formula (1) and (2) as, v → α B → = m α v α 2 r α Rearrange the above expression to find r α as, r α = m α v α q α B The initial momentum of alpha particle and proton before collision is, p i = m α v α + m p v p Here, v α is the velocity of the alpha particle. v p is the velocity of proton. The final momentum of proton and alpha particle after collision is, p f = m α v 0 α + m p v 0 p Here, v 0 α is the velocity of the alpha particle after collision. v 0 p is the velocity of proton after collision. Apply the law of conservation of momentum for the elastic collision for proton and alpha particle is, p i = p f 1 2 m α v α + 1 2 m p v 2 p = 1 2 m α v 2 0 α + 1 2 m p v 0 α 2 m α v α + m p v p = m α v 0 α + m p v 0 p Here, m p is the mass of proton. m α is the mass of alpha particle. v α is the velocity of alpha particle before collision.. v 0 p is the velocity of proton after collision. v 0 α is the velocity of alpha particle after collision

9th Edition

ISBN: 8220100546310

Author: Jewett

Publisher: CENGAGE L

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Magnetic Force

A magnetic force arises when a charged particle or a current-carrying conductor is placed in a magnetic field. It is created because of the movement of the charged particles.

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Chapter 29, Problem 29.63AP

To determine

The radius of the alpha particle’s trajectory.

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Chapter 29 Solutions

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The radius of the alpha particle’s trajectory.

Solution Summary: The author explains the formula to calculate the magnetic force acting on an alpha particle.

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The radius of the alpha particle’s trajectory.

Chapter 29 Solutions