The de Broglie wavelength is given by

Options

A. `p=(2pih)/(lamda)`
B. `p=(h)/(2lamda)`
C. `p=(2pi)/(hlamda)`
D. `p=(2pi)/(lamda)`

Explanation

To find the de Broglie wavelength, we start with the fundamental formula provided by de Broglie. The de Broglie wavelength (\(\lambda\)) is given by the equation:

\[ \lambda = \frac{h}{mv} \]

Where:
- \(h\) is Planck's constant,
- \(m\) is the mass of the particle,
- \(v\) is the velocity of the particle.

### Step 1: Understand the Formula
The de Broglie wavelength relates the wavelength of a particle to its momentum. The momentum \(p\) of a particle can be expressed as:

\[ p = mv \]

### Step 2: Substitute Momentum into the Wavelength Formula
We can rewrite the de Broglie wavelength in terms of momentum:

\[ \lambda = \frac{h}{p} \]

### Step 3: Express Planck's Constant in Terms of \(\hbar\)
Planck's constant \(h\) can also be expressed in terms of the reduced Planck's constant (\(\hbar\)), where:

\[ \hbar = \frac{h}{2\pi} \]

Thus, we can express \(h\) as:

\[ h = 2\pi\hbar \]

### Step 4: Substitute \(h\) into the Wavelength Formula
Now, substituting \(h\) into the de Broglie wavelength formula gives:

\[ \lambda = \frac{2\pi\hbar}{p} \]

### Step 5: Final Expression for Momentum
If we need to express momentum \(p\) in terms of the wavelength \(\lambda\), we rearrange the equation:

\[ p = \frac{2\pi\hbar}{\lambda} \]

### Conclusion
Thus, the de Broglie wavelength can be expressed as:

\[ \lambda = \frac{h}{mv} \quad \text{or} \quad \lambda = \frac{2\pi\hbar}{p} \]