Which one of the following statements is not ture about de-Broglie waves ?

Options

A. All atomic particles in motion have waves of a definite wavelength associated with them
B. Higher the momentum , the longer is the wave-length
C. Faster the perticle , the shorter is the wave-length
D. For the same volecity , a heavier particle has a shorter wavelength

Answer

To solve the question, we need to analyze the statements regarding de-Broglie waves and identify which one is not true.

### Step-by-Step Solution:

1. **Understanding de-Broglie Waves**:
- De-Broglie waves describe the wave-particle duality of matter, suggesting that every moving particle has an associated 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. **Evaluating the Statements**:
- **Statement 1**: "All atomic particles in motion have waves of definite wavelength associated with them."
- This statement is **true** because all particles in motion indeed have a de-Broglie wavelength.

- **Statement 2**: "Higher the momentum, the longer is the wavelength."
- This statement is **false**. According to the de-Broglie wavelength formula, as momentum increases, the wavelength decreases (λ is inversely proportional to P). Thus, this statement is incorrect.

- **Statement 3**: "Faster the particle, the shorter is the wavelength."
- This statement is **true**. As the speed of the particle increases, its momentum increases, leading to a shorter wavelength.

- **Statement 4**: "For the same velocity, a heavier particle has a shorter wavelength."
- This statement is **true**. For the same velocity, a heavier particle has greater momentum, which results in a shorter wavelength.

3. **Conclusion**:
- The only statement that is not true about de-Broglie waves is **Statement 2**: "Higher the momentum, the longer is the wavelength."

### Final Answer:
The statement that is not true about de-Broglie waves is: **"Higher the momentum, the longer is the wavelength."**

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