Consider an Ar atom trapped in square box with length 1 m. the Ar atom is equal to thermal energy: 3KBT/2 at 25ºC. a) Use the model of a particle in a box and assume the particl
Consider an Ar atom trapped in square box with length 1 m. the Ar atom is equal to thermal energy: 3KBT/2 at 25ºC. a) Use the model of a particle in a box and assume the particl
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![Question 2
Consider an Ar atom trapped in square box with length 1 m. Assume that the energy of
the Ar atom is equal to thermal energy: 3kgT/2 at 25°C.
a) Use the model of a particle in a box and assume the particle is at the state: n = nx = ly
= nz, calculaten of the above system.
b) What is the energy separation between the states (n, n, n) and (n + 1, n, n).
c) Assume that all the energy of the particle is from kinetic energy. Calculate the de
Broglie wavelength of the particle.
d) Based on your answers above, would you treat this particle classically or quantumly?
Explain your answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdbba0bc5-061e-4b6f-84b9-d685d90bc038%2F3dc80d3a-f669-43d3-91c0-6d54acdc4f2c%2Fb1p2gg_processed.png&w=3840&q=75)
Transcribed Image Text:Question 2
Consider an Ar atom trapped in square box with length 1 m. Assume that the energy of
the Ar atom is equal to thermal energy: 3kgT/2 at 25°C.
a) Use the model of a particle in a box and assume the particle is at the state: n = nx = ly
= nz, calculaten of the above system.
b) What is the energy separation between the states (n, n, n) and (n + 1, n, n).
c) Assume that all the energy of the particle is from kinetic energy. Calculate the de
Broglie wavelength of the particle.
d) Based on your answers above, would you treat this particle classically or quantumly?
Explain your answer.
Expert Solution
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Step 1
The particle in a box model describes a particle, free to move in a small space surrounded by impenetrable barriers. The energy for a particle in a box is given by the expression:
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