Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 7, Problem 26E

(a)

To determine

The angular frequency of particle

(b)

To determine

Energy difference of the orbit.

(c)

To determine

The decrease of radius in single orbit

(d)

To determine

The time in which electron radiates all energy

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(2nx sin \1.50. 2nz Consider the case of a 3-dimensional particle-in-a-box. Given: 4 = sin(ny) sin 2.00. What is the energy of the system? O 6h?/8m O 4h²/8m O 3h2/8m O none are correct
(d) Prove that for a classical particle moving from left to right in a box with constant speed v, the average position = (1/T) ff x(t) dt = L/2, where T L/v is the time taken to move from left to right. And = : (1/T) S²x² (t) dt L²/3. Hint: Only consider a particle moving from left x = 0 to right x = L = and do not include the bouncing motion from right to left. The results for left to right are independent of the sense of motion and therefore the same results apply to all the bounces, so that we can prove it for just one sense of motion. Thus, the classical result is obtained from the Quantum solution when n >> 1. That is, for large energies compared to the minimum energy of the wave-particle system. This is usually referred to as the Classical Limit for Large Quantum Numbers.
A particle with mass m is in a field and has the state (in spherical coordinates) : Where N > 0 and a > 0 are fixed numbers. Determine the average kinetic energy of the particles.

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