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Which of the following is true for 2px, 2py and 2pz orbitals of a H-atom?
- a)All are eigen functions of Lz
- b)2px and 2pz orbitals are eigen functions of Lz
- c)Only 2px 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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Which of the following is true for 2px, 2py and 2pz orbitals of a H-at...
Explanation:
The 2px, 2py, and 2pz orbitals of a hydrogen atom are the three degenerate orbitals, which means that they have the same energy and are mathematically equivalent. However, they differ in their spatial orientation, which is determined by the values of the quantum numbers l and m.
The quantum number l specifies the angular momentum of an electron in an atom and determines the shape of the orbital. For l = 1, the shape of the orbital is dumbbell-shaped, and it has three possible orientations in space, designated as 2px, 2py, and 2pz, depending on the value of the quantum number m.
The quantum number m specifies the orientation of the orbital in space and can take on integer values ranging from -l to +l, including zero. For l = 1, the possible values of m are -1, 0, and +1, corresponding to the 2px, 2py, and 2pz orbitals, respectively.
The operator Lz represents the z-component of the angular momentum operator, which measures the angular momentum of an electron in the z-direction. The eigenfunctions of Lz are the wave functions that satisfy the equation Lzψ = mℏψ, where m is the eigenvalue of the operator Lz.
Therefore, the correct option is D) Only 2pz orbital is an eigenfunction of Lz, as its wave function has a non-zero value for m = +1, which is the eigenvalue of the operator Lz. The wave functions of 2px and 2py orbitals have a non-zero value for m = 0, which is not an eigenvalue of the operator Lz.
The 2px, 2py, and 2pz orbitals of a hydrogen atom are the three degenerate orbitals, which means that they have the same energy and are mathematically equivalent. However, they differ in their spatial orientation, which is determined by the values of the quantum numbers l and m.
The quantum number l specifies the angular momentum of an electron in an atom and determines the shape of the orbital. For l = 1, the shape of the orbital is dumbbell-shaped, and it has three possible orientations in space, designated as 2px, 2py, and 2pz, depending on the value of the quantum number m.
The quantum number m specifies the orientation of the orbital in space and can take on integer values ranging from -l to +l, including zero. For l = 1, the possible values of m are -1, 0, and +1, corresponding to the 2px, 2py, and 2pz orbitals, respectively.
The operator Lz represents the z-component of the angular momentum operator, which measures the angular momentum of an electron in the z-direction. The eigenfunctions of Lz are the wave functions that satisfy the equation Lzψ = mℏψ, where m is the eigenvalue of the operator Lz.
Therefore, the correct option is D) Only 2pz orbital is an eigenfunction of Lz, as its wave function has a non-zero value for m = +1, which is the eigenvalue of the operator Lz. The wave functions of 2px and 2py orbitals have a non-zero value for m = 0, which is not an eigenvalue of the operator Lz.
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Which of the following is true for 2px, 2py and 2pz orbitals of a H-atom?a)All are eigen functions of Lzb)2px and 2pz orbitals are eigen functions of Lzc)Only 2px orbital is an eigen function of Lzd)Only 2pz orbital is an eigen function of LzCorrect answer is option 'D'. Can you explain this answer?
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