Bragg`s equation will have bno solution if :

Options

A. ` lambda gt 2d`
B. ` lambda lt 2d`
C. ` lambda gt d`
D. ` lambda = d`

Explanation

To determine when Bragg's equation has no solution, we start by recalling the equation itself:

**Bragg's Equation:**
\[ n\lambda = 2d \sin \theta \]

Where:
- \( n \) is the order of reflection (an integer),
- \( \lambda \) is the wavelength of the incident wave,
- \( d \) is the distance between the crystal planes,
- \( \theta \) is the angle of incidence.

### Step-by-Step Solution:

1. **Understanding the Range of sin θ**:
- The sine function, \( \sin \theta \), has a range of values from -1 to 1. This means that for any angle \( \theta \), the maximum value of \( \sin \theta \) can be 1.

2. **Setting Up the Condition for No Solution**:
- For Bragg's equation to have no solution, the right side of the equation, \( 2d \sin \theta \), must exceed the maximum possible value of \( n\lambda \). This occurs when:
\[ 2d \sin \theta > n\lambda \]
- Since \( \sin \theta \) can be at most 1, the maximum value of \( 2d \sin \theta \) is \( 2d \).

3. **Analyzing the Condition**:
- If we set the condition for no solution as:
\[ n\lambda > 2d \]
- Rearranging this gives:
\[ \lambda > \frac{2d}{n} \]
- For the first order reflection (where \( n = 1 \)), this simplifies to:
\[ \lambda > 2d \]

4. **Conclusion**:
- Therefore, Bragg's equation will have no solution if the wavelength \( \lambda \) is greater than twice the distance between the crystal planes \( d \).

### Final Answer:
Bragg's equation will have no solution if:
\[ \lambda > 2d \]