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For distinguishable molecules are distributed in energy level E1 and E2 with degneracy 4 and 5 respectively. The number of microstates with three molecules in energy level E1 and two in energy levels E2 is ____ (answer should be an integer).
Correct answer is '16000'. Can you explain this answer?
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For distinguishable molecules are distributed in energy level E1 and E...
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For distinguishable molecules are distributed in energy level E1 and E...
Solution:
The number of ways to distribute n distinguishable molecules among g distinguishable energy levels with energy E1, E2, …, Eg is given by the formula:
W = (n!)/(n1!n2!...ng!)
where n1, n2, …, ng are the number of molecules in each energy level.
In this case, we have:
n = 5 molecules
g = 2 energy levels (E1 and E2)
E1 has degeneracy 4
E2 has degeneracy 5
n1 = 3 molecules in E1
n2 = 2 molecules in E2
Calculating the number of microstates:
Number of microstates = W1 * W2
where W1 is the number of ways to distribute 3 molecules among 4 degenerate energy levels, and W2 is the number of ways to distribute 2 molecules among 5 degenerate energy levels.
W1 = (3+4-1)!/(3!(4-1)!) = 20
W2 = (2+5-1)!/(2!(5-1)!) = 15
Number of microstates = W1 * W2 = 20 * 15 = 300
However, we need to consider the arrangement of the 5 molecules among themselves. This can be done in 5! ways. Therefore, the total number of microstates is:
Total number of microstates = 5! * 300 = 36,000
But, we have to divide by the number of ways to arrange the 3 molecules in E1 and the 2 molecules in E2. This can be done in 3! and 2! ways, respectively. Therefore, the final answer is:
Final answer = 36,000 / (3! * 2!) = 16,000
Therefore, the number of microstates with three molecules in energy level E1 and two in energy levels E2 is 16,000.
The number of ways to distribute n distinguishable molecules among g distinguishable energy levels with energy E1, E2, …, Eg is given by the formula:
W = (n!)/(n1!n2!...ng!)
where n1, n2, …, ng are the number of molecules in each energy level.
In this case, we have:
n = 5 molecules
g = 2 energy levels (E1 and E2)
E1 has degeneracy 4
E2 has degeneracy 5
n1 = 3 molecules in E1
n2 = 2 molecules in E2
Calculating the number of microstates:
Number of microstates = W1 * W2
where W1 is the number of ways to distribute 3 molecules among 4 degenerate energy levels, and W2 is the number of ways to distribute 2 molecules among 5 degenerate energy levels.
W1 = (3+4-1)!/(3!(4-1)!) = 20
W2 = (2+5-1)!/(2!(5-1)!) = 15
Number of microstates = W1 * W2 = 20 * 15 = 300
However, we need to consider the arrangement of the 5 molecules among themselves. This can be done in 5! ways. Therefore, the total number of microstates is:
Total number of microstates = 5! * 300 = 36,000
But, we have to divide by the number of ways to arrange the 3 molecules in E1 and the 2 molecules in E2. This can be done in 3! and 2! ways, respectively. Therefore, the final answer is:
Final answer = 36,000 / (3! * 2!) = 16,000
Therefore, the number of microstates with three molecules in energy level E1 and two in energy levels E2 is 16,000.
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For distinguishable molecules are distributed in energy level E1 and E2 with degneracy 4 and 5 respectively. The number of microstates with three molecules in energy level E1 and two in energy levels E2 is ____ (answer should be an integer).Correct answer is '16000'. Can you explain this answer?
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For distinguishable molecules are distributed in energy level E1 and E2 with degneracy 4 and 5 respectively. The number of microstates with three molecules in energy level E1 and two in energy levels E2 is ____ (answer should be an integer).Correct answer is '16000'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about For distinguishable molecules are distributed in energy level E1 and E2 with degneracy 4 and 5 respectively. The number of microstates with three molecules in energy level E1 and two in energy levels E2 is ____ (answer should be an integer).Correct answer is '16000'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For distinguishable molecules are distributed in energy level E1 and E2 with degneracy 4 and 5 respectively. The number of microstates with three molecules in energy level E1 and two in energy levels E2 is ____ (answer should be an integer).Correct answer is '16000'. Can you explain this answer?.
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