de-Broglie equation tells about

Options

A. the relation between electron and nucleus
B. the relation between electron and proton
C. the relation between electron and neutron
D. electrons having duel nature of wave and particle.

Answer

To answer the question "What does the de-Broglie equation tell us about?", we can break down the solution into several steps:

### Step 1: Understanding the de-Broglie Equation
The de-Broglie equation is given by the formula:
\[ \lambda = \frac{h}{p} \]
where:
- \( \lambda \) is the wavelength,
- \( h \) is Planck's constant, and
- \( p \) is the momentum of the particle.

### Step 2: Dual Nature of Matter
The de-Broglie equation illustrates the concept of wave-particle duality, which suggests that particles, such as electrons, exhibit both wave-like and particle-like properties. This means that electrons can behave like waves under certain conditions and like particles under others.

### Step 3: Implications of the Equation
From the equation, we can infer that:
- As the momentum \( p \) of a particle increases, the wavelength \( \lambda \) decreases. This means faster-moving particles have shorter wavelengths.
- Conversely, particles with lower momentum have longer wavelengths, indicating a wave-like behavior.

### Step 4: Relation to Electrons and Nucleus
The question specifically asks about the relation to electrons and the nucleus. The de-Broglie equation helps us understand that electrons, which orbit the nucleus, do not just behave as discrete particles but also have a wave nature. This duality is crucial in quantum mechanics, particularly in explaining electron behavior in atoms.

### Step 5: Conclusion
Based on the understanding of the de-Broglie equation and its implications, we can conclude that it tells us about the dual nature of electrons, which is best captured in option D: "electrons having dual nature of wave and particle."

### Final Answer
The de-Broglie equation tells us about the dual nature of electrons, indicating that they exhibit both wave-like and particle-like properties.

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