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 determine which statement is not true about de-Broglie waves, we will analyze each option provided. The de-Broglie hypothesis states that every moving particle has an associated wave, and the wavelength (λ) of this wave is inversely proportional to its momentum (p).

### Step-by-Step Solution:

1. **Understanding de-Broglie Waves**:
- According to de-Broglie's theory, every particle in motion has a wavelength associated with it, given by the formula:
\[ \lambda = \frac{h}{p} \]
where \( h \) is Planck's constant and \( p \) is the momentum of the particle.

2. **Analyzing Option 1**:
- **Statement**: "All atomic particles in motion have waves of a definite wavelength associated with them."
- **Analysis**: This statement is true as it directly reflects the de-Broglie hypothesis.

3. **Analyzing Option 2**:
- **Statement**: "Higher the momentum, the longer is the wavelength."
- **Analysis**: This statement is false. According to the de-Broglie relation, wavelength is inversely proportional to momentum. Therefore, if momentum increases, the wavelength decreases. This makes this statement incorrect.

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

5. **Analyzing Option 4**:
- **Statement**: "For the same velocity, a heavier particle has a shorter wavelength."
- **Analysis**: This statement is also true. If the velocity is constant and the mass increases, the momentum increases, resulting in a shorter wavelength.

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

### Final Answer:
**Option 2** is not true about de-Broglie waves.