Which of the following expressions gives the de-Broglie relationship?

Options

A. `(h)/(mv) = p`
B. `lambda = (h)/(mv)`
C. `lambda = (h)/(mp)`
D. `lambda m = (v)/(p)`

Explanation

To solve the question regarding the de-Broglie relationship, we will follow these steps:

### Step 1: Understand the de-Broglie Relationship
The de-Broglie relationship describes the wave-particle duality of matter. It states that every moving particle or object has an associated wavelength.

### Step 2: Write the de-Broglie Equation
The fundamental equation given by de Broglie is:
\[ \lambda = \frac{h}{p} \]
where:
- \(\lambda\) is the wavelength,
- \(h\) is Planck's constant,
- \(p\) is the momentum of the particle.

### Step 3: Define Momentum
Momentum (\(p\)) is defined as the product of mass (\(m\)) and velocity (\(v\)):
\[ p = mv \]

### Step 4: Substitute Momentum in the de-Broglie Equation
Substituting the expression for momentum into the de-Broglie equation gives:
\[ \lambda = \frac{h}{mv} \]

### Step 5: Identify the Correct Expression
Now, we need to identify which of the provided options matches the derived expression. The correct expression for the de-Broglie wavelength is:
\[ \lambda = \frac{h}{mv} \]
This corresponds to option B in the question.

### Conclusion
Thus, the expression that gives the de-Broglie relationship is:
\[ \lambda = \frac{h}{mv} \]