The de-Broglie wavelength associated with a particle of momentum p is given as :

Options

A. p/h
B. h/p
C. hp
D. None of these

Answer

To find the de-Broglie wavelength associated with a particle of momentum \( p \), we can follow these steps:

### Step 1: Understand the Concept of de-Broglie Wavelength
The de-Broglie wavelength (\( \lambda \)) is a concept that arises from the wave-particle duality of matter. It suggests that every moving particle or object has an associated wavelength. This wavelength is inversely proportional to the momentum of the particle.

### Step 2: Recall the Relationship Between Energy, Mass, and Momentum
For a photon, which is a massless particle, the relationship between energy (\( E \)), momentum (\( p \)), and wavelength (\( \lambda \)) is given by:
\[ E = pc \]
where \( c \) is the speed of light.

### Step 3: Express Energy in Terms of Wavelength
The energy of a photon can also be expressed in terms of its wavelength:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant.

### Step 4: Equate the Two Expressions for Energy
Since both expressions represent the energy of the photon, we can set them equal to each other:
\[ pc = \frac{hc}{\lambda} \]

### Step 5: Rearrange the Equation to Solve for Wavelength
To find the de-Broglie wavelength, we can rearrange the equation:
\[ \lambda = \frac{h}{p} \]

### Conclusion
Thus, the de-Broglie wavelength associated with a particle of momentum \( p \) is given by:
\[ \lambda = \frac{h}{p} \]