Select the correct statement (s) :

Options

A. Heisenberg's principle is applicable to stationary electron
B. Pauli,s exclusion principle is not applicable to photons
C. For and electron the product of velocity and principle quantum number will be independent to principle quantum number
D. Quantum numbers l and m determine the value of angular wave function

Answer

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

### Step-by-Step Solution:

1. **Statement A: Heisenberg's principle is applicable to the stationary electron.**
- **Analysis:** Heisenberg's Uncertainty Principle states that the uncertainty in position (Δx) and the uncertainty in momentum (Δp) cannot both be precisely measured at the same time. Mathematically, it is expressed as Δx * Δp ≥ h / (4π). For a stationary electron, its momentum is zero (since momentum p = mass * velocity, and velocity is zero). Therefore, the principle does not apply to a stationary electron because there is no momentum to measure.
- **Conclusion:** This statement is **incorrect**.

2. **Statement B: Pauli's exclusion principle is not applicable to photons.**
- **Analysis:** The Pauli Exclusion Principle states that no two electrons can occupy the same quantum state simultaneously within an atom. This principle is specific to fermions (like electrons) and does not apply to bosons (like photons). Photons can occupy the same state, hence this statement is true.
- **Conclusion:** This statement is **correct**.

3. **Statement C: For an electron, the product of velocity and principal quantum number will be independent of the principal quantum number.**
- **Analysis:** According to Bohr's model, the velocity of an electron in a hydrogen atom is given by \( v_n = 2.18 \times 10^6 \frac{Z}{n} \) m/s, where Z is the atomic number and n is the principal quantum number. If we multiply the velocity by the principal quantum number (n), we get \( v_n \cdot n = 2.18 \times 10^6 \cdot Z \). This product depends on Z but is independent of n.
- **Conclusion:** This statement is **correct**.

4. **Statement D: Quantum numbers l and m determine the value of the angular wave function.**
- **Analysis:** The angular wave function (part of the wave function in quantum mechanics) is indeed determined by the angular momentum quantum number (l) and the magnetic quantum number (m). The wave function can be expressed as a product of radial and angular components, where the angular part depends on l and m.
- **Conclusion:** This statement is **correct**.

### Final Selection of Correct Statements:
- **Correct Statements:** B, C, D
- **Incorrect Statement:** A