The angular wave function of which orbital with not disturb by the variation with azimuthal angle only

Options

A. `1s` and `2s`
B. `2p_(z)` and `2d_(z)^(2)`
C. `2p_(x)` and `3d_(z)^(2)`
D. `2p_(x)` and `2s`

Answer

To solve the question regarding which orbital's angular wave function is not disturbed by the variation with the azimuthal angle, we can follow these steps:

### Step 1: Understand the Angular Wave Function
The angular wave function describes how the probability density of finding an electron varies with angles in three-dimensional space. It is typically expressed in terms of spherical coordinates, which include the polar angle (θ) and the azimuthal angle (φ).

### Step 2: Identify the Orbitals
The main types of orbitals are s, p, d, and f:
- **s orbitals**: These are spherical and have no angular dependence. Their wave function depends only on the radial distance (r).
- **p orbitals**: These have a dumbbell shape and depend on both r and θ.
- **d orbitals**: These have more complex shapes and also depend on both r and θ.
- **f orbitals**: These are even more complex and depend on r, θ, and φ.

### Step 3: Analyze the s Orbital
The s orbital is unique because it is spherical. This means that the electron density is uniform in all directions, and it does not change with variations in the azimuthal angle (φ). Therefore, the angular wave function for the s orbital does not depend on φ.

### Step 4: Conclusion
Since the s orbital is the only one that does not vary with the azimuthal angle, we can conclude that the angular wave function of the s orbital will not be disturbed by variations in the azimuthal angle.

### Final Answer
The angular wave function of the **s orbital** will not be disturbed by the variation with the azimuthal angle only.

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