What is the ratio of the kinetic energies for an alpha...

Name: What is the ratio of the kinetic energies for an alpha particle and a beta particle if both make tracks with the same radius of curvature in a magnetic field, oriented perpendicular to the paths of the particles?
Uploaded: 2021-11-13T02:12:04-08:00
Duration: 3 min 37 s
Channel: Nishant Kumar
Description: What is the ratio of the kinetic energies for an alpha particle and a beta particle if both make tracks with the same radius of curvature in a magnetic field, oriented perpendicular to the paths of the particles?

What is the ratio of the kinetic energies for an alpha particle and a beta particle if both make tracks with the same radius of curvature in a magnetic field, oriented perpendicular to the paths of the particles?

Transcript

00:01 Here we have to find the ratio of kinetic energies for an alpha particle and a beta particle and both have same radius of curvature in a magnetic field which is perpendicular to their paths so radius of a charge in a magnetic field when the charge is moving perpendicular to field is given by r equal to m v upon qb where m is the mass v is speed q is charge and b is magnetic field now for the alpha particle and for the beta particle the radius is same.

00:43 So we have r alpha equal to r beta which means this is mass of alpha particle times speed of alpha particle upon charge q of alpha particle times magnetic field b.

00:59 Similarly for beta particle mass of beta particle times speed of beta particle divided by charge of beta particle times magnetic field so b cancels out and we have m alpha v alpha upon m beta v beta equal to q alpha upon q beta now charge on alpha particle is plus 2 e and for beta particle it's e the magnitude of charge and beta particle is e because it is electron so we have m alpha particle and v alpha upon m beta v beta equal to 2 now m alpha v alpha is the momentum of alpha particle so we can write it as p alpha similarly m beta v beta is momentum of beta particle so it's a p beta is equal to two now we know that kinetic energy k is given by p square upon 2m where m is the mass of particle and p is the momentum of particle so the kinetic energy of alpha upon kinetic ratio of beta will be equal to p alpha square upon 2m alpha divided by p beta square upon 2m so we have p alpha upon p alpha square into m alpha upon m beta now p alpha is the momentum of alpha particle and p beta is momentum of beta particle and the ratio is equal to 2 as we saw about so we have k alpha upon k beta equal to 2 square into mass of alpha particle divided by the mass of beta particle so let's see 4 mass of alpha particle is 6 .6 4 into 10 to the power minus 27 kilogram and mass of beta particle which is simply electron is 9 .11 into 10 to the power minus 31 kg so the ratio is equal to 2 .92 into 10 to the power...

Question

What is the ratio of the kinetic energies for an alpha particle and a beta particle if both make tracks with the same radius of curvature in a magnetic field, oriented perpendicular to the paths of the particles?

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