The Maxwell speed distribution function is given by: f(v): = 3 m (2πKBT) 4πv² e-mv²/2kgT i. Show that the average speed of the molecule is given by (v) = √√8kBT/лm. A valve connecting a first chamber, containing a mixture of 10% ³He and 90% 4He, is opened to a second chamber, which is under vacuum. The diameter of the valve is small compared to the mean free path of the atoms, and the number of atoms escaping from the first to the second chamber will depend on the species. iii. ii. Calculate the ratio of the number of ³He and 4He atoms that have escaped the first chamber. How many times, approximately, does this procedure need to be repeated to produce a mixture of 30% ³He?
The Maxwell speed distribution function is given by: f(v): = 3 m (2πKBT) 4πv² e-mv²/2kgT i. Show that the average speed of the molecule is given by (v) = √√8kBT/лm. A valve connecting a first chamber, containing a mixture of 10% ³He and 90% 4He, is opened to a second chamber, which is under vacuum. The diameter of the valve is small compared to the mean free path of the atoms, and the number of atoms escaping from the first to the second chamber will depend on the species. iii. ii. Calculate the ratio of the number of ³He and 4He atoms that have escaped the first chamber. How many times, approximately, does this procedure need to be repeated to produce a mixture of 30% ³He?
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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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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![The Maxwell speed distribution function is given by:
ƒ(v) =
3
m
(2 KT)² 4πv² e-mv²/2kBT
i. Show that the average speed of the molecule is given by (v) = /8kgT/πm.
A valve connecting a first chamber, containing a mixture of 10% ³He and 90% *He, is opened to a second
chamber, which is under vacuum. The diameter of the valve is small compared to the mean free path of the
atoms, and the number of atoms escaping from the first to the second chamber will depend on the species.
ii.
iii.
Calculate the ratio of the number of ³He and 4He atoms that have escaped the first chamber.
How many times, approximately, does this procedure need to be repeated to produce a mixture of
30% ³He?
[Hint: Use the flux Ⓡ = n(v) where n is the number density n = =N/V]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9df25b32-664d-4e03-ac77-887e1e433afe%2Fab958f97-9122-4302-bd13-54f1d303ade2%2Fvp0rzs_processed.png&w=3840&q=75)
Transcribed Image Text:The Maxwell speed distribution function is given by:
ƒ(v) =
3
m
(2 KT)² 4πv² e-mv²/2kBT
i. Show that the average speed of the molecule is given by (v) = /8kgT/πm.
A valve connecting a first chamber, containing a mixture of 10% ³He and 90% *He, is opened to a second
chamber, which is under vacuum. The diameter of the valve is small compared to the mean free path of the
atoms, and the number of atoms escaping from the first to the second chamber will depend on the species.
ii.
iii.
Calculate the ratio of the number of ³He and 4He atoms that have escaped the first chamber.
How many times, approximately, does this procedure need to be repeated to produce a mixture of
30% ³He?
[Hint: Use the flux Ⓡ = n(v) where n is the number density n = =N/V]
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