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or a quantum particle confined inside a cubic box of side L, the ground state energy is given by E0. The energy of the first excited state is
- a)2E0
- b)2√E0
- c)3E0
- d)6E0
Correct answer is option 'A'. Can you explain this answer?
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or a quantum particle confined inside a cubic box of side L, the groun...
E0 is correct.
For a particle confined inside a cubic box of side L, the energy levels are given by:
E(n1, n2, n3) = [(n1^2 + n2^2 + n3^2) * h^2] / [8mL^2]
where n1, n2, and n3 are integers that specify the quantum numbers for the three dimensions, h is the Planck constant, and m is the mass of the particle.
The ground state corresponds to n1 = n2 = n3 = 1, and thus has energy:
E0 = [(1^2 + 1^2 + 1^2) * h^2] / [8mL^2] = (3/8) * (h^2 / mL^2)
The first excited state corresponds to one of the quantum numbers being 2, and the other two being 1. Without loss of generality, let n1 = 2, and n2 = n3 = 1. Then the energy of this state is:
E1 = [(2^2 + 1^2 + 1^2) * h^2] / [8mL^2] = (6/8) * (h^2 / mL^2) = (3/4) * E0
Therefore, the correct answer is (b) 2E0.
For a particle confined inside a cubic box of side L, the energy levels are given by:
E(n1, n2, n3) = [(n1^2 + n2^2 + n3^2) * h^2] / [8mL^2]
where n1, n2, and n3 are integers that specify the quantum numbers for the three dimensions, h is the Planck constant, and m is the mass of the particle.
The ground state corresponds to n1 = n2 = n3 = 1, and thus has energy:
E0 = [(1^2 + 1^2 + 1^2) * h^2] / [8mL^2] = (3/8) * (h^2 / mL^2)
The first excited state corresponds to one of the quantum numbers being 2, and the other two being 1. Without loss of generality, let n1 = 2, and n2 = n3 = 1. Then the energy of this state is:
E1 = [(2^2 + 1^2 + 1^2) * h^2] / [8mL^2] = (6/8) * (h^2 / mL^2) = (3/4) * E0
Therefore, the correct answer is (b) 2E0.
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or a quantum particle confined inside a cubic box of side L, the ground state energy is given by E0. The energy of the first excited state isa)2E0b)2√E0c)3E0d)6E0Correct answer is option 'A'. Can you explain this answer?
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or a quantum particle confined inside a cubic box of side L, the ground state energy is given by E0. The energy of the first excited state isa)2E0b)2√E0c)3E0d)6E0Correct answer is option 'A'. Can you explain this answer? for IIT JAM 2024 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about or a quantum particle confined inside a cubic box of side L, the ground state energy is given by E0. The energy of the first excited state isa)2E0b)2√E0c)3E0d)6E0Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for IIT JAM 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for or a quantum particle confined inside a cubic box of side L, the ground state energy is given by E0. The energy of the first excited state isa)2E0b)2√E0c)3E0d)6E0Correct answer is option 'A'. Can you explain this answer?.
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