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If energy of a state in 2D-box is 17h2/8ml2, degeneracy would be?
Correct answer is '2'. Can you explain this answer?
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Most Upvoted Answer
If energy of a state in 2D-box is 17h2/8ml2, degeneracy would be?Corre...
Explanation:
The energy of a state in a 2D-box is given by the formula:
E = (nx2 + ny2)h2/8mL2
where nx and ny are the quantum numbers in the x- and y-directions, respectively, h is Planck's constant, m is the mass of the particle, and L is the length of the box in both directions.
Given:
E = 17h2/8mL2
To find:
Degeneracy of the state.
Solution:
The degeneracy of a state is the number of ways that state can be realized. In the case of a 2D-box, the degeneracy is given by the number of combinations of nx and ny that give the same energy.
Let's first simplify the given energy expression:
E = 17h2/8mL2 = (2.125h2/mL2)
Now, we need to find all possible combinations of nx and ny that satisfy the equation:
nx2 + ny2 = 2.125(L/h)2
We can use the fact that nx and ny are integers to find the possible combinations:
nx = 1, ny = 2
nx = 2, ny = 1
These two combinations give the same energy, so the degeneracy of the state is 2.
Answer:
The degeneracy of the state is 2.
The energy of a state in a 2D-box is given by the formula:
E = (nx2 + ny2)h2/8mL2
where nx and ny are the quantum numbers in the x- and y-directions, respectively, h is Planck's constant, m is the mass of the particle, and L is the length of the box in both directions.
Given:
E = 17h2/8mL2
To find:
Degeneracy of the state.
Solution:
The degeneracy of a state is the number of ways that state can be realized. In the case of a 2D-box, the degeneracy is given by the number of combinations of nx and ny that give the same energy.
Let's first simplify the given energy expression:
E = 17h2/8mL2 = (2.125h2/mL2)
Now, we need to find all possible combinations of nx and ny that satisfy the equation:
nx2 + ny2 = 2.125(L/h)2
We can use the fact that nx and ny are integers to find the possible combinations:
nx = 1, ny = 2
nx = 2, ny = 1
These two combinations give the same energy, so the degeneracy of the state is 2.
Answer:
The degeneracy of the state is 2.
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Community Answer
If energy of a state in 2D-box is 17h2/8ml2, degeneracy would be?Corre...
4²+1²
1²+4²
so the ans is 2
1²+4²
so the ans is 2
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If energy of a state in 2D-box is 17h2/8ml2, degeneracy would be?Correct answer is '2'. Can you explain this answer?
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