Which one of the following statements is NOT true for de Broglie waves?

Options

A. All atomic particles in motion have wavelength of a definite wavelength associated with them
B. The higher the momentum, the longer is the wavelength
C. The faster the particle, the shorter is the wavelength
D. For the same velocity, a heavier particle has a shorter wavelength

Explanation

To solve the question regarding which statement is NOT true for de Broglie waves, we will analyze each of the provided options based on our understanding of de Broglie wavelength.

### Step-by-Step Solution:

1. **Understand de Broglie Wavelength**:
The de Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{p} \]
where \(h\) is Planck's constant and \(p\) is the momentum of the particle.

2. **Analyze Each Statement**:
We will evaluate each option to determine its validity.

- **Option A**: "All atomic particles in motion have a definite wavelength associated with them."
- This statement is true. According to de Broglie's hypothesis, every moving particle has a wavelength associated with it.

- **Option B**: "Higher the momentum, the longer is the wavelength."
- This statement is NOT true. According to the de Broglie wavelength formula, as momentum increases, the wavelength decreases. Thus, higher momentum corresponds to a shorter wavelength.

- **Option C**: "Faster the particle, the shorter the wavelength."
- This statement is true. As the speed of the particle increases, its momentum increases, leading to a shorter wavelength.

- **Option D**: "For the same velocity, a heavier particle has a shorter wavelength."
- This statement is also true. For a given velocity, if the mass (and thus momentum) of the particle increases, the wavelength decreases.

3. **Conclusion**:
After evaluating all the statements, we find that **Option B** is the one that is NOT true for de Broglie waves.

### Final Answer:
The statement that is NOT true for de Broglie waves is **Option B**: "Higher the momentum, the longer is the wavelength."

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