Radial part of the wave function depends on quantum numbers

Options

A. n and s
B. 1 and m
C. 1 and s
D. n and 1

Answer

To determine the quantum numbers that the radial part of the wave function depends on, we can follow these steps:

### Step 1: Understand the Wave Function
The wave function, often denoted as ψ (psi), describes the quantum state of a particle. It can be separated into two parts: the radial part and the angular part.

### Step 2: Identify the Quantum Numbers
The wave function is influenced by several quantum numbers:
- **Principal Quantum Number (n)**: This quantum number indicates the energy level and the average distance of the electron from the nucleus. It is a positive integer (n = 1, 2, 3,...).
- **Azimuthal Quantum Number (l)**: This quantum number determines the shape of the orbital and is related to the angular momentum of the electron. It can take values from 0 to (n-1).

### Step 3: Determine the Dependence of the Radial Part
The radial part of the wave function depends on both the principal quantum number (n) and the azimuthal quantum number (l). The radial wave function describes how the probability density of finding an electron varies with distance from the nucleus.

### Step 4: Conclusion
Thus, the radial part of the wave function depends on:
- Principal Quantum Number (n)
- Azimuthal Quantum Number (l)

### Final Answer
The radial part of the wave function depends on the principal quantum number (n) and the azimuthal quantum number (l).

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