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The following is true of 2px, 2py and 2pz orbitals of a H-atom:
- a)All are eigen functions of Lz
- b)Only 2px and 2pz orbitals are eigen functions of Lz
- c)Only 2py orbital is an eigen function of Lz
- d)Only 2pz orbital is an eigen function of Lz.
Correct answer is option 'D'. Can you explain this answer?
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The following is true of 2px, 2py and 2pz orbitals of a H-atom:a)All a...
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The following is true of 2px, 2py and 2pz orbitals of a H-atom:a)All a...
Explanation:
The angular momentum operator, L, describes the rotational motion of an atom or molecule. It has three components: Lx, Ly, and Lz, which correspond to rotations around the x, y, and z axes, respectively. Each component of angular momentum has associated eigenfunctions, which are the wavefunctions that represent the quantized angular momentum states.
2px, 2py, and 2pz Orbitals
- The 2px, 2py, and 2pz orbitals are three of the five atomic orbitals in the second energy level of a hydrogen atom. These orbitals have different shapes and orientations in space.
- The 2px orbital is aligned along the x-axis, the 2py orbital is aligned along the y-axis, and the 2pz orbital is aligned along the z-axis.
- The wavefunctions that describe these orbitals are eigenfunctions of the angular momentum operator.
Lz Operator
- The Lz operator represents the z-component of the angular momentum operator. It describes the rotational motion around the z-axis.
- The eigenfunctions of the Lz operator represent the quantized angular momentum states with respect to the z-axis.
Eigenfunctions of Lz
- The eigenfunctions of the Lz operator are the wavefunctions that represent the quantized angular momentum states around the z-axis.
- For the 2px and 2pz orbitals, the wavefunctions are eigenfunctions of the Lz operator, as these orbitals have non-zero angular momentum around the z-axis.
- However, the 2py orbital does not have any angular momentum around the z-axis, as it is aligned along the y-axis. Therefore, the 2py orbital is not an eigenfunction of the Lz operator.
Correct Answer
- The correct answer is option 'D' - Only the 2pz orbital is an eigenfunction of the Lz operator.
- The 2px and 2pz orbitals have non-zero angular momentum around the z-axis, making them eigenfunctions of the Lz operator.
- The 2py orbital does not have any angular momentum around the z-axis, so it is not an eigenfunction of the Lz operator.
The angular momentum operator, L, describes the rotational motion of an atom or molecule. It has three components: Lx, Ly, and Lz, which correspond to rotations around the x, y, and z axes, respectively. Each component of angular momentum has associated eigenfunctions, which are the wavefunctions that represent the quantized angular momentum states.
2px, 2py, and 2pz Orbitals
- The 2px, 2py, and 2pz orbitals are three of the five atomic orbitals in the second energy level of a hydrogen atom. These orbitals have different shapes and orientations in space.
- The 2px orbital is aligned along the x-axis, the 2py orbital is aligned along the y-axis, and the 2pz orbital is aligned along the z-axis.
- The wavefunctions that describe these orbitals are eigenfunctions of the angular momentum operator.
Lz Operator
- The Lz operator represents the z-component of the angular momentum operator. It describes the rotational motion around the z-axis.
- The eigenfunctions of the Lz operator represent the quantized angular momentum states with respect to the z-axis.
Eigenfunctions of Lz
- The eigenfunctions of the Lz operator are the wavefunctions that represent the quantized angular momentum states around the z-axis.
- For the 2px and 2pz orbitals, the wavefunctions are eigenfunctions of the Lz operator, as these orbitals have non-zero angular momentum around the z-axis.
- However, the 2py orbital does not have any angular momentum around the z-axis, as it is aligned along the y-axis. Therefore, the 2py orbital is not an eigenfunction of the Lz operator.
Correct Answer
- The correct answer is option 'D' - Only the 2pz orbital is an eigenfunction of the Lz operator.
- The 2px and 2pz orbitals have non-zero angular momentum around the z-axis, making them eigenfunctions of the Lz operator.
- The 2py orbital does not have any angular momentum around the z-axis, so it is not an eigenfunction of the Lz operator.
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The following is true of 2px, 2py and 2pz orbitals of a H-atom:a)All are eigen functions of Lzb)Only 2px and 2pz orbitals are eigen functions of Lzc)Only 2py orbital is an eigen function of Lzd)Only 2pz orbital is an eigen function of Lz.Correct answer is option 'D'. Can you explain this answer?
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