Bragg's law for X-rays is

Options

A. `d sin theta=2nlambda`
B. `2d sin theta=nlambda`
C. `n sin theta =2lambdad`
D. None of these

Explanation

To solve the question regarding Bragg's law for X-rays, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Bragg's Law**:
Bragg's law describes the condition for constructive interference of X-rays scattered by a crystal lattice. It is essential to understand the geometry involved in the scattering process.

2. **Identify the Variables**:
- Let \( d \) be the spacing between the atomic planes in the crystal.
- Let \( \theta \) be the angle of incidence (and reflection).
- Let \( n \) be an integer (order of reflection).
- Let \( \lambda \) be the wavelength of the X-rays.

3. **Path Difference Calculation**:
When X-rays hit the crystal planes, the path difference between the rays reflected from adjacent planes can be derived from the geometry of the situation. The path difference \( \Delta \) for the rays reflected from the first and second planes is given by:
\[ \Delta = 2d \sin \theta \]
This is because the ray travels down to the second plane and back up.

4. **Condition for Constructive Interference**:
For constructive interference to occur, the path difference must be an integer multiple of the wavelength \( \lambda \):
\[ \Delta = n \lambda \]

5. **Equating the Two Expressions**:
By equating the two expressions for path difference, we have:
\[ 2d \sin \theta = n \lambda \]

6. **Conclusion**:
This equation \( 2d \sin \theta = n \lambda \) is known as Bragg's law. It indicates the conditions under which constructive interference occurs for X-rays scattered by a crystal.

7. **Selecting the Correct Option**:
From the options provided, the correct statement of Bragg's law for X-rays is:
\[ 2d \sin \theta = n \lambda \]

### Final Answer:
The correct option for Bragg's law for X-rays is:
\[ 2d \sin \theta = n \lambda \]