(3) Let us consider a particle that can take three energies —ɛ, 0, ɛ. This particle is immersed in abath of constant temperature T.(a) Calculate the probability P for this particle to have the energy -ε. Evaluate this probabilityP in the limits of T = 0 and T = ∞o.(b) Calculate the partition function Z and the Helmholtz free energy F.

Based on the information in the image, we can solve for the probability (P) of a particle having…

Answered: (3) Let us consider a particle that can…

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter7: Quantum Mechanics

Section: Chapter Questions

Problem 7.3CYU: Check Your Understanding For the particle in the example, find the probability Of locating it 0 and...

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Similar questions

Check Your Understanding For the particle in the example, find the probability Of locating it 0 and L/4.
Check Your Understanding If a=3+4i , what is the product a* a?
Compute |(x,t)|2 for the function (x,t)=(x)sint, where is a real constant.
A simple model of a radioactive nuclear decay assumes that a-particles are trapped inside a well of nuclear potential that walls are the barriers of a finite width 2.0 fm and height 30.0 MeV. Find the tunneling probability across the potential barrier of the wall for a-particles having kinetic energy (a) 29.0 MeV and (b) 20.0 MeV. The mass of the a -particle is m=6.641027kg.
(a) Repeat Exercise 31.2, and convert the energy to joules or calories. (b) If all of this energy is converted to thermal energy in the gas, what is its temperature increase, assuming 50.0 cm3 of ideal gas at 0.250atm pressure? (The small answer is consistent with the fact that the energy is large on a quantum mechanical scale but small on a macroscopic scale.)
A particle of mass m is confined to a box of width L. If the particle is in the first excited state, what are the probabilities of finding the particle in a region of width0.020 L around the given point x: (a) x=0.25L; (b) x=040L; (c) 0.75L and (d) x=0.90L.
In STM, an elevation of the tip above the surface being scanned can be determined with a great precision, because the tunneling-electron current between surface atoms and the atoms of the tip is extremely sensitive to the variation of the separation gap between them from point to point along the surface. Assuming that the tunneling-electron current is in direct proportion to the tunneling probability and that the tunneling probability is to a gotxi approximation expressed by the exponential function e2L with =10.0/nm , determine the ratio of the tunneling current when the tip is 0.500 nm above the surface to the current when the tip is 0.515 nm above the surface.
Can we measure the energy of a free localized particle with complete precision?
When an electron and a proton of the same kinetic energy encounter a barrier of the same height and width, which one of them will tunnel through the barrier more easily? Why?
A 12.0-eV electron encounters a barrier of height 15.0 eV. If the probability of the electron tunneling through the barrier is 2.5 %, find its width.
A particle of mass m confined to a box of width L is in its first excited state 2(x). (a) Find its average position (which is the expectation value of the position). (b) Where is the particle most likely to found?
Explain the difference between time-dependent and independent SchrÖdinger's equations.

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