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.