In a diffraction experiment, X-rays of wavelength 0.14 nm were used on a crystal. 'n' is the order of diffraction that occurs at an angle `theta` of `19.5^(0)`. If the interplanar distance is 0.42nm. n value is `(sin 19.5^(0) = 0.333)`

Options

A. 1
B. 2
C. 3
D. 4

Answer

To solve the problem, we will use Bragg's Law, which relates the wavelength of X-rays, the angle of diffraction, and the interplanar distance in a crystal. The formula is given by:

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

Where:
- \( n \) is the order of diffraction,
- \( \lambda \) is the wavelength of the X-rays,
- \( d \) is the interplanar distance,
- \( \theta \) is the angle of diffraction.

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Wavelength \( \lambda = 0.14 \, \text{nm} \)
- Interplanar distance \( d = 0.42 \, \text{nm} \)
- Angle \( \theta = 19.5^\circ \)
- \( \sin 19.5^\circ = 0.333 \)

2. **Rearrange Bragg's Law**:
To find \( n \), we can rearrange the formula:
\[ n = \frac{2d \sin \theta}{\lambda} \]

3. **Substitute the Values into the Formula**:
Now, we substitute the known values into the rearranged formula:
\[ n = \frac{2 \times 0.42 \, \text{nm} \times 0.333}{0.14 \, \text{nm}} \]

4. **Calculate the Numerator**:
First, calculate the numerator:
\[ 2 \times 0.42 \times 0.333 = 0.28068 \, \text{nm} \]

5. **Calculate \( n \)**:
Now divide the numerator by the wavelength:
\[ n = \frac{0.28068 \, \text{nm}}{0.14 \, \text{nm}} = 2.004857 \]

6. **Approximate \( n \)**:
Since \( n \) must be an integer, we can approximate \( 2.004857 \) to \( 2 \).

### Final Answer:
The order of diffraction \( n \) is approximately \( 2 \).

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