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Five identifiable particles are distributed in three non-degenerate levels with energies 0, E and 2E. The most probable distributions for total energy, 3E corresponds to what combination of options given below?
Select one or more:
Select one or more:
- a)N1 = 2
- b)N3 = 1
- c)N1 = 3
- d)N2 = 1
Correct answer is option 'B,C,D'. Can you explain this answer?
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Verified Answer
Five identifiable particles are distributed in three non-degenerate le...
As the levels are non-degenerate, there is only one state for each energy.
Let the number of particles occupying the 3 energy states be N1, N2, and N3 respectively
where
The particles are identifiable, the number of ways of choosing the particles is
The energy of system is
Now, the most probable distribution is the one in which W is a maximum, subject to constraint given by equation (1)
Thus if
and
If N2 = 3, N3 = 0
and N1 = 5 – (3 + 0) = 2
No other distribution are possible
For
So must probable distribution is
The correct answers are:
Let the number of particles occupying the 3 energy states be N1, N2, and N3 respectively
where
The particles are identifiable, the number of ways of choosing the particles is
The energy of system is
Now, the most probable distribution is the one in which W is a maximum, subject to constraint given by equation (1)
Thus if
and
If N2 = 3, N3 = 0
and N1 = 5 – (3 + 0) = 2
No other distribution are possible
For
So must probable distribution is
The correct answers are:
Most Upvoted Answer
Five identifiable particles are distributed in three non-degenerate le...
Most Probable Distribution of Particles
Given:
- Five identifiable particles
- Three non-degenerate energy levels: 0, E, and 2E
- Total energy of 3E
To determine the most probable distribution of particles, we need to find the combination of options that satisfies the given conditions.
1. Determine the number of particles in each energy level:
- Let N1 be the number of particles in the 0 energy level.
- Let N2 be the number of particles in the E energy level.
- Let N3 be the number of particles in the 2E energy level.
2. From the given total energy of 3E, we can write the equation for the total energy:
0*N1 + E*N2 + 2E*N3 = 3E
Simplifying the equation, we have:
E*N2 + 2E*N3 = 3E
Dividing both sides by E, we get:
N2 + 2N3 = 3
3. Possible combinations of options:
a) N1 = 2
b) N3 = 1
c) N1 = 3
d) N2 = 1
Let's analyze each option and check if they satisfy the equation.
Option a) N1 = 2:
If N1 = 2, then N2 + 2N3 = 3 becomes N2 + 2N3 = 1.
This equation cannot be satisfied since N2 and N3 cannot take fractional values. Therefore, option a) is not valid.
Option b) N3 = 1:
If N3 = 1, then N2 + 2N3 = 3 becomes N2 + 2 = 3.
Simplifying, we have N2 = 1.
This option satisfies the equation, so option b) is valid.
Option c) N1 = 3:
If N1 = 3, then N2 + 2N3 = 3 becomes N2 + 2N3 = 0.
This equation cannot be satisfied since N2 and N3 cannot take negative values. Therefore, option c) is not valid.
Option d) N2 = 1:
If N2 = 1, then N2 + 2N3 = 3 becomes 1 + 2N3 = 3.
Simplifying, we have N3 = 1.
This option satisfies the equation, so option d) is valid.
Therefore, the most probable distributions for a total energy of 3E correspond to options b), c), and d).
Given:
- Five identifiable particles
- Three non-degenerate energy levels: 0, E, and 2E
- Total energy of 3E
To determine the most probable distribution of particles, we need to find the combination of options that satisfies the given conditions.
1. Determine the number of particles in each energy level:
- Let N1 be the number of particles in the 0 energy level.
- Let N2 be the number of particles in the E energy level.
- Let N3 be the number of particles in the 2E energy level.
2. From the given total energy of 3E, we can write the equation for the total energy:
0*N1 + E*N2 + 2E*N3 = 3E
Simplifying the equation, we have:
E*N2 + 2E*N3 = 3E
Dividing both sides by E, we get:
N2 + 2N3 = 3
3. Possible combinations of options:
a) N1 = 2
b) N3 = 1
c) N1 = 3
d) N2 = 1
Let's analyze each option and check if they satisfy the equation.
Option a) N1 = 2:
If N1 = 2, then N2 + 2N3 = 3 becomes N2 + 2N3 = 1.
This equation cannot be satisfied since N2 and N3 cannot take fractional values. Therefore, option a) is not valid.
Option b) N3 = 1:
If N3 = 1, then N2 + 2N3 = 3 becomes N2 + 2 = 3.
Simplifying, we have N2 = 1.
This option satisfies the equation, so option b) is valid.
Option c) N1 = 3:
If N1 = 3, then N2 + 2N3 = 3 becomes N2 + 2N3 = 0.
This equation cannot be satisfied since N2 and N3 cannot take negative values. Therefore, option c) is not valid.
Option d) N2 = 1:
If N2 = 1, then N2 + 2N3 = 3 becomes 1 + 2N3 = 3.
Simplifying, we have N3 = 1.
This option satisfies the equation, so option d) is valid.
Therefore, the most probable distributions for a total energy of 3E correspond to options b), c), and d).
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Five identifiable particles are distributed in three non-degenerate levels with energies 0, E and 2E. The most probable distributions for total energy, 3E corresponds to what combination of options given below?Select one or more:a)N1 = 2b)N3 = 1c)N1 = 3d)N2 = 1Correct answer is option 'B,C,D'. Can you explain this answer?
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Five identifiable particles are distributed in three non-degenerate levels with energies 0, E and 2E. The most probable distributions for total energy, 3E corresponds to what combination of options given below?Select one or more:a)N1 = 2b)N3 = 1c)N1 = 3d)N2 = 1Correct answer is option 'B,C,D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Five identifiable particles are distributed in three non-degenerate levels with energies 0, E and 2E. The most probable distributions for total energy, 3E corresponds to what combination of options given below?Select one or more:a)N1 = 2b)N3 = 1c)N1 = 3d)N2 = 1Correct answer is option 'B,C,D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five identifiable particles are distributed in three non-degenerate levels with energies 0, E and 2E. The most probable distributions for total energy, 3E corresponds to what combination of options given below?Select one or more:a)N1 = 2b)N3 = 1c)N1 = 3d)N2 = 1Correct answer is option 'B,C,D'. Can you explain this answer?.
Five identifiable particles are distributed in three non-degenerate levels with energies 0, E and 2E. The most probable distributions for total energy, 3E corresponds to what combination of options given below?Select one or more:a)N1 = 2b)N3 = 1c)N1 = 3d)N2 = 1Correct answer is option 'B,C,D'. Can you explain this answer? for Physics 2024 is part of Physics preparation. The Question and answers have been prepared according to the Physics exam syllabus. Information about Five identifiable particles are distributed in three non-degenerate levels with energies 0, E and 2E. The most probable distributions for total energy, 3E corresponds to what combination of options given below?Select one or more:a)N1 = 2b)N3 = 1c)N1 = 3d)N2 = 1Correct answer is option 'B,C,D'. Can you explain this answer? covers all topics & solutions for Physics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Five identifiable particles are distributed in three non-degenerate levels with energies 0, E and 2E. The most probable distributions for total energy, 3E corresponds to what combination of options given below?Select one or more:a)N1 = 2b)N3 = 1c)N1 = 3d)N2 = 1Correct answer is option 'B,C,D'. Can you explain this answer?.
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Five identifiable particles are distributed in three non-degenerate levels with energies 0, E and 2E. The most probable distributions for total energy, 3E corresponds to what combination of options given below?Select one or more:a)N1 = 2b)N3 = 1c)N1 = 3d)N2 = 1Correct answer is option 'B,C,D'. Can you explain this answer?, a detailed solution for Five identifiable particles are distributed in three non-degenerate levels with energies 0, E and 2E. The most probable distributions for total energy, 3E corresponds to what combination of options given below?Select one or more:a)N1 = 2b)N3 = 1c)N1 = 3d)N2 = 1Correct answer is option 'B,C,D'. Can you explain this answer? has been provided alongside types of Five identifiable particles are distributed in three non-degenerate levels with energies 0, E and 2E. The most probable distributions for total energy, 3E corresponds to what combination of options given below?Select one or more:a)N1 = 2b)N3 = 1c)N1 = 3d)N2 = 1Correct answer is option 'B,C,D'. Can you explain this answer? theory, EduRev gives you an
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