Repeat Exercise 27.15 for the case in which the particle is a proton rather than an electron.

Name: Problem 16, Chapter 27: University Physics with Modern Physics
Uploaded: 2019-03-26T01:42:39-08:00
Duration: 3 min 30 s
Channel: Ceren Uzun
Description: Repeat Exercise 27.15 for the case in which the particle is a proton rather than an electron.

step 1 This is chapter 27 problem number 16. We are given a proton that is moving along a circular traj

Repeat Exercise 27.15 for the case in which the particle is...

Key Concepts

de Broglie Wavelength

The de Broglie wavelength characterizes the wave–like nature of a particle and is inversely proportional to its momentum. Because momentum depends on both the energy and the mass of the particle, substituting an electron with a proton results in a significantly shorter de Broglie wavelength for the same kinetic energy. This difference can lead to observable changes in diffraction and interference phenomena during scattering.

Coulomb Potential and Particle Charge

When dealing with charged particles, the Coulomb potential describes their electrostatic interactions, which can be either attractive or repulsive depending on the charges involved. Changing the particle from an electron to a proton not only alters the mass but may also affect the nature of the interaction if the sign change plays a role in the context of the potential. Understanding how charge influences the potential energy is crucial for accurately modeling scattering processes involving different particles.

Schrödinger Equation in Scattering

This key concept involves solving the time?independent Schrödinger equation to understand how quantum particles behave under the influence of a potential. It is the foundation for describing scattering processes, where the kinetic term (which depends on the particle’s mass) and the potential term determine the resulting wave function and its asymptotic forms.

Particle Mass and its Effects

In quantum mechanics, the mass of a particle is a critical parameter since it affects the kinetic energy and, consequently, the evolution of the wave function. Changing the particle from an electron to a proton (which is much heavier) alters the effective momentum and penetration properties, thereby modifying factors such as the scattering amplitudes and cross sections in any quantum scattering problem.

Transcript

00:01 This is chapter 27 problem number 16.

00:03 We are given a proton that is moving along a circular trajectory from a point a to b.

00:10 And we know the initial velocity.

00:14 It's 1 .41 times 10 ,000 per second.

00:18 And, well, this circular motion is due to the magnetic force acting on the proton.

00:27 So as you know, the direction has to be along the centipedal direction so that with the initial velocity, the initial speed, the particle would go along the circular trajectory.

00:40 So this is the direction of f sub b.

00:42 We are asked to calculate the magnitude and the direction of the magnetic field.

00:50 So just simply from right -hand rule, we can say that the direction of b, direction of b has to be out of the ward or the screen, right, for a positive charge.

01:08 And in order to determine the magnitude of it, as you know, your f sub b is qvb, since there is 90 degree angle between the velocity vector and the force.

01:21 I'm adding sign 90 here, which is one.

01:23 This has to be equal to from newton's second law, mv squared over r when you have a circular motion.

01:29 So from here, if we want to go to the magnitude of the magnetic field, then we divide both sides by a qv.

01:37 Qv, these are going to cancel up.

01:39 You're going to have the magnetic field to be.

01:42 These are going to cancel mv over qr...

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