For first order X–ray diffraction if lattice constant is `3 xx 10^(–8)` cm and glancing angle is 30°, then the value of `lambda` will be :

Options

A. `1.5xx10^(-8)cm`
B. `3xx10^(-8)cm`
C. `1.5xx10^(-8)m`
D. `3xx10^(-8)m`

Answer

To solve the problem of finding the wavelength (λ) of X-rays in first order diffraction, we will use Bragg's law, which states:

\[ 2d \sin \theta = n \lambda \]

Where:
- \( d \) is the lattice constant,
- \( \theta \) is the glancing angle,
- \( n \) is the order of diffraction (which is 1 for first order),
- \( \lambda \) is the wavelength.

### Step-by-Step Solution:

1. **Identify the given values:**
- Lattice constant \( d = 3 \times 10^{-8} \) cm
- Glancing angle \( \theta = 30^\circ \)
- Order of diffraction \( n = 1 \)

2. **Substitute the values into Bragg's law:**
\[ 2d \sin \theta = n \lambda \]
Substituting the known values:
\[ 2(3 \times 10^{-8}) \sin(30^\circ) = 1 \cdot \lambda \]

3. **Calculate \( \sin(30^\circ) \):**
\[ \sin(30^\circ) = \frac{1}{2} \]

4. **Substitute \( \sin(30^\circ) \) into the equation:**
\[ 2(3 \times 10^{-8}) \left(\frac{1}{2}\right) = \lambda \]

5. **Simplify the equation:**
\[ 2 \times 3 \times 10^{-8} \times \frac{1}{2} = 3 \times 10^{-8} \]
Therefore, we have:
\[ \lambda = 3 \times 10^{-8} \text{ cm} \]

### Final Answer:
The value of \( \lambda \) is \( 3 \times 10^{-8} \) cm.

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