The wave mechanical model of an atom is based upon which of the following equations ?

Options

A. Schrodinger’s equation
B. de Broglie’s equation
C. Heisenberg’ uncertainty principle
D. All of the above

Explanation

To answer the question regarding which equations the wave mechanical model of an atom is based upon, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Wave Mechanical Model**:
- The wave mechanical model of the atom describes electrons not just as particles but also as waves. This dual nature is crucial for understanding atomic structure.

2. **Identifying Key Contributors**:
- The wave mechanical model is primarily based on the contributions of three key figures in quantum mechanics: Louis de Broglie, Werner Heisenberg, and Erwin Schrödinger.

3. **De Broglie's Contribution**:
- Louis de Broglie proposed that particles, such as electrons, exhibit wave-like properties. He formulated the de Broglie wavelength equation:
\[ \lambda = \frac{h}{p} \]
where \( \lambda \) is the wavelength, \( h \) is Planck's constant, and \( p \) is the momentum of the particle.

4. **Heisenberg's Uncertainty Principle**:
- Werner Heisenberg introduced the Uncertainty Principle, which states that it is impossible to simultaneously know the exact position and momentum of an electron. This is expressed mathematically as:
\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]
where \( \Delta x \) is the uncertainty in position and \( \Delta p \) is the uncertainty in momentum.

5. **Schrödinger's Wave Equation**:
- Erwin Schrödinger developed a wave equation that describes how the quantum state of a physical system changes over time. This equation is fundamental to the wave mechanical model and leads to the concept of orbitals and quantum numbers.

6. **Conclusion**:
- The wave mechanical model of the atom is based on the contributions of de Broglie, Heisenberg, and Schrödinger. Therefore, the correct answer to the question is that it is based on all of the above equations.

### Final Answer:
The wave mechanical model of an atom is based upon all of the following equations: de Broglie's equation, Heisenberg's uncertainty principle, and Schrödinger's wave equation. Thus, the correct option is **"All of the above"**.

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