Select the correct statement (s) :

Options

A. Radial function `[R(r)]` is a part of wave function which depends upon quantum number n the nucleus
B. Angular function depends only on the direction, and is independent to the distance form the nucleus
C. `Psi^(2)(r,theta,Phi)` is the probability density of finding the electronat a particular point in space
D. Radial distribution function `(4pir^(2)R^(2))` gives the probability of the electron being present at a distance r from the nucleus

Answer

To solve the question of selecting the correct statements regarding atomic structure, we will analyze each statement step by step:

### Step 1: Analyze the First Statement
**Statement:** "Radial function r is a part of the wave function which depends on the quantum number of the nucleus."

- **Explanation:** The radial function is indeed a part of the wave function (ψ), but it does not depend solely on the quantum number of the nucleus. Instead, it depends on both the principal quantum number (N) and the azimuthal quantum number (L). Therefore, this statement is **incorrect**.

### Step 2: Analyze the Second Statement
**Statement:** "Angular function depends only on the direction and is independent of the distance from the nucleus."

- **Explanation:** The angular function is indeed dependent on the azimuthal quantum number (L) and the magnetic quantum number (M), which determine the shape and orientation of the orbitals, respectively. It does not depend on the distance from the nucleus, which is the role of the radial function. Therefore, this statement is **correct**.

### Step 3: Analyze the Third Statement
**Statement:** "Radial psi square is the probability density of finding the electron at a particular point in space."

- **Explanation:** The wave function (ψ) squared (ψ²) represents the probability density of finding an electron at a specific point in space. This statement is correct as it aligns with the interpretation of the wave function in quantum mechanics. Therefore, this statement is **correct**.

### Step 4: Analyze the Fourth Statement
**Statement:** "Radial distribution function that is 4 pi R² R² gives the probability of the electron being present at a distance r from the nucleus."

- **Explanation:** The radial distribution function is indeed given by the expression 4πR², where R is the radial distance from the nucleus. This function gives the probability of finding the electron at a distance r from the nucleus, considering the volume element in spherical coordinates. Therefore, this statement is **correct**.

### Conclusion
Based on the analysis:
- **Statement A** is incorrect.
- **Statements B, C, and D** are correct.

### Final Answer
The correct statements are B, C, and D.

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