Veriation of momentum of perticle (p) with associated de-Broglie wavelength `(lambda) ` is shown correctly by

Options

A.
B.
C.
D.

Answer

To solve the problem of the variation of momentum \( p \) of a particle with its associated de Broglie wavelength \( \lambda \), we can follow these steps:

### Step-by-Step Solution:

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

2. **Rearranging the Formula**:
We can rearrange the formula to express momentum \( p \) in terms of wavelength \( \lambda \):
\[ p = \frac{h}{\lambda} \]

3. **Identifying the Relationship**:
From the rearranged formula, we can see that momentum \( p \) is inversely proportional to the wavelength \( \lambda \). This means that as the wavelength increases, the momentum decreases, and vice versa.

4. **Graphical Representation**:
The relationship \( p \cdot \lambda = h \) can be recognized as the equation of a rectangular hyperbola. In a rectangular hyperbola, the product of two variables is constant. This means that if we plot \( p \) on one axis and \( \lambda \) on the other, the graph will show a hyperbolic shape.

5. **Conclusion**:
Based on the analysis, the correct graph that represents the variation of momentum \( p \) with the associated de Broglie wavelength \( \lambda \) is a rectangular hyperbola. Therefore, the correct option is **Option A**.