PHYSICS F./SCI... W/MOD V.II W/KIT
PHYSICS F./SCI... W/MOD V.II W/KIT
4th Edition
ISBN: 9780134819884
Author: GIANCOLI
Publisher: PEARSON
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Chapter 38, Problem 25P
To determine

Whether the results for the ground state are consistent with uncertainly principle by calculating the product ΔpΔx for the particle in a box with rigid walls.

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(a) Show that the spread of velocities caused by the uncertainty principle does not have measurable consequences for macroscopic objects (objects that are large compared with atoms) by considering a 100-g racquetball confined to a room 15 m on a side. Assume the ball is moving at 2.0 m/s along the x axis.
(c) Light of wavelength 450 nm is emitted by an electron in an atom behaving as a lightly damped simple harmonic oscillator with a Q value of 2×107. Find the natural frequency of the system in radians per second.
(I) Suppose the wave function for an electron at time t = 0 is given by (x,0) = /2/L sin(57x/L). Which one of the following is the wave function at time t? (a) p(x, t) = Vž sin(57x/L) cos(Est/h) (b) p(x, t) = Vž sin(57x/L)e-iEst/h (c) Both (a) and (b) above are appropriate ways to write the wave function. (d) None of the above. (II) The wave function for an electron at timet =0 is given by (x,0) = /? sin(57x/L). Which one of the following is true about the probability density, |p(x, t)², after time t? (a) [h(x, t)* = { sin²(57x/L) cos²(Est/h). (b) |Þ(x, t)P = Z sin?(57x/L)e¬i2Est/h. (c) |Þ(x,t)[² = } sin (57x/L) which is time-independent. (d) None of the above. 4

Chapter 38 Solutions

PHYSICS F./SCI... W/MOD V.II W/KIT

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