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For a particle in 3 dimensional box
- a)The number of quantum numbers is equal to dimensions of potential distribution
- b)The spin quantum number does not arise from Schrodinger wave equations
- c)The symmetry of box leads to degeneracy
- d)If we consider spin also for fermions then the degeneracy of energy levels become twice
Correct answer is option 'A,B,C,D'. Can you explain this answer?
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For a particle in 3 dimensional boxa)The number of quantum numbers is ...
The correct answers are: The number of quantum numbers is equal to dimensions of potential distribution, The symmetry of box leads to degeneracy, The spin quantum number does not arise from Schrodinger wave equations. Spherical polar coordinates are used in the solution of the hydrogen atom Schrodinger equation because: The Schrodinger equation is then separable into 3 ordinary differential equations. If we consider spin also for fermions then the degeneracy of energy levels become twice.
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For a particle in 3 dimensional boxa)The number of quantum numbers is ...
The Number of Quantum Numbers
The number of quantum numbers in a system is equal to the dimensions of the potential distribution. In the case of a particle in a 3-dimensional box, the potential distribution is defined by the dimensions of the box. Since there are three dimensions (length, width, and height) in the box, there are also three quantum numbers that describe the particle's energy levels and wavefunction in each dimension. These quantum numbers are typically denoted as n_x, n_y, and n_z, where n represents the energy level in each dimension.
The Spin Quantum Number
The spin quantum number is a fundamental property of particles, which describes their intrinsic angular momentum. It does not arise from the Schrödinger wave equation, but rather from the relativistic theory of quantum mechanics known as the Dirac equation. The spin quantum number can take on two values: +1/2 or -1/2, representing the two possible spin states of a particle. It is an additional quantum number that complements the spatial quantum numbers (n_x, n_y, and n_z) in fully describing the quantum state of a particle.
Symmetry and Degeneracy
The symmetry of the box in which the particle is confined leads to degeneracy in the energy levels. In a 3-dimensional box, the energy levels are determined by the quantum numbers (n_x, n_y, and n_z), and each quantum number can take on any positive integer value. However, due to the symmetry of the box, certain combinations of quantum numbers can give rise to the same energy level. This results in degeneracy, where multiple different quantum states have the same energy.
Degeneracy of Energy Levels with Spin
If we consider the spin of particles, such as electrons, which are fermions, the degeneracy of energy levels becomes twice. This is due to the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously. Since the spin quantum number can take on two values (+1/2 or -1/2), each energy level can accommodate two electrons with opposite spins. Therefore, the degeneracy of each energy level in a 3-dimensional box is effectively doubled when spin is considered for fermions.
The number of quantum numbers in a system is equal to the dimensions of the potential distribution. In the case of a particle in a 3-dimensional box, the potential distribution is defined by the dimensions of the box. Since there are three dimensions (length, width, and height) in the box, there are also three quantum numbers that describe the particle's energy levels and wavefunction in each dimension. These quantum numbers are typically denoted as n_x, n_y, and n_z, where n represents the energy level in each dimension.
The Spin Quantum Number
The spin quantum number is a fundamental property of particles, which describes their intrinsic angular momentum. It does not arise from the Schrödinger wave equation, but rather from the relativistic theory of quantum mechanics known as the Dirac equation. The spin quantum number can take on two values: +1/2 or -1/2, representing the two possible spin states of a particle. It is an additional quantum number that complements the spatial quantum numbers (n_x, n_y, and n_z) in fully describing the quantum state of a particle.
Symmetry and Degeneracy
The symmetry of the box in which the particle is confined leads to degeneracy in the energy levels. In a 3-dimensional box, the energy levels are determined by the quantum numbers (n_x, n_y, and n_z), and each quantum number can take on any positive integer value. However, due to the symmetry of the box, certain combinations of quantum numbers can give rise to the same energy level. This results in degeneracy, where multiple different quantum states have the same energy.
Degeneracy of Energy Levels with Spin
If we consider the spin of particles, such as electrons, which are fermions, the degeneracy of energy levels becomes twice. This is due to the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously. Since the spin quantum number can take on two values (+1/2 or -1/2), each energy level can accommodate two electrons with opposite spins. Therefore, the degeneracy of each energy level in a 3-dimensional box is effectively doubled when spin is considered for fermions.
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For a particle in 3 dimensional boxa)The number of quantum numbers is equal to dimensions of potential distributionb)The spin quantum number does not arise from Schrodinger wave equationsc)The symmetry of box leads to degeneracyd)If we consider spin also for fermions then the degeneracy of energy levels become twiceCorrect answer is option 'A,B,C,D'. Can you explain this answer?
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For a particle in 3 dimensional boxa)The number of quantum numbers is equal to dimensions of potential distributionb)The spin quantum number does not arise from Schrodinger wave equationsc)The symmetry of box leads to degeneracyd)If we consider spin also for fermions then the degeneracy of energy levels become twiceCorrect answer is option 'A,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 For a particle in 3 dimensional boxa)The number of quantum numbers is equal to dimensions of potential distributionb)The spin quantum number does not arise from Schrodinger wave equationsc)The symmetry of box leads to degeneracyd)If we consider spin also for fermions then the degeneracy of energy levels become twiceCorrect answer is option 'A,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 For a particle in 3 dimensional boxa)The number of quantum numbers is equal to dimensions of potential distributionb)The spin quantum number does not arise from Schrodinger wave equationsc)The symmetry of box leads to degeneracyd)If we consider spin also for fermions then the degeneracy of energy levels become twiceCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
For a particle in 3 dimensional boxa)The number of quantum numbers is equal to dimensions of potential distributionb)The spin quantum number does not arise from Schrodinger wave equationsc)The symmetry of box leads to degeneracyd)If we consider spin also for fermions then the degeneracy of energy levels become twiceCorrect answer is option 'A,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 For a particle in 3 dimensional boxa)The number of quantum numbers is equal to dimensions of potential distributionb)The spin quantum number does not arise from Schrodinger wave equationsc)The symmetry of box leads to degeneracyd)If we consider spin also for fermions then the degeneracy of energy levels become twiceCorrect answer is option 'A,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 For a particle in 3 dimensional boxa)The number of quantum numbers is equal to dimensions of potential distributionb)The spin quantum number does not arise from Schrodinger wave equationsc)The symmetry of box leads to degeneracyd)If we consider spin also for fermions then the degeneracy of energy levels become twiceCorrect answer is option 'A,B,C,D'. Can you explain this answer?.
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For a particle in 3 dimensional boxa)The number of quantum numbers is equal to dimensions of potential distributionb)The spin quantum number does not arise from Schrodinger wave equationsc)The symmetry of box leads to degeneracyd)If we consider spin also for fermions then the degeneracy of energy levels become twiceCorrect answer is option 'A,B,C,D'. Can you explain this answer?, a detailed solution for For a particle in 3 dimensional boxa)The number of quantum numbers is equal to dimensions of potential distributionb)The spin quantum number does not arise from Schrodinger wave equationsc)The symmetry of box leads to degeneracyd)If we consider spin also for fermions then the degeneracy of energy levels become twiceCorrect answer is option 'A,B,C,D'. Can you explain this answer? has been provided alongside types of For a particle in 3 dimensional boxa)The number of quantum numbers is equal to dimensions of potential distributionb)The spin quantum number does not arise from Schrodinger wave equationsc)The symmetry of box leads to degeneracyd)If we consider spin also for fermions then the degeneracy of energy levels become twiceCorrect answer is option 'A,B,C,D'. Can you explain this answer? theory, EduRev gives you an
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