For the diffraction from a crystal with `lamda=1Å` and Bragg's angle `theta=60^(@)`, then for the second order diffraction 'd' will be :

Options

A. 1.15 Å
B. 0.75 Å
C. 0.55 Å
D. 2.1 Å

Explanation

To solve the problem, we will use Bragg's Law, which is given by the equation:

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

Where:
- \( n \) is the order of diffraction,
- \( \lambda \) is the wavelength of the incident wave,
- \( d \) is the distance between the crystal planes,
- \( \theta \) is the Bragg's angle.

### Step-by-step solution:

1. **Identify the given values:**
- Wavelength \( \lambda = 1 \, \text{Å} = 1 \times 10^{-10} \, \text{m} \)
- Bragg's angle \( \theta = 60^\circ \)
- Order of diffraction \( n = 2 \)

2. **Write down Bragg's Law:**
\[ n\lambda = d \sin \theta \]

3. **Rearrange the equation to solve for \( d \):**
\[ d = \frac{n\lambda}{\sin \theta} \]

4. **Substitute the known values into the equation:**
\[ d = \frac{2 \times 1 \times 10^{-10}}{\sin 60^\circ} \]

5. **Calculate \( \sin 60^\circ \):**
\[ \sin 60^\circ = \frac{\sqrt{3}}{2} \]

6. **Substitute \( \sin 60^\circ \) into the equation:**
\[ d = \frac{2 \times 1 \times 10^{-10}}{\frac{\sqrt{3}}{2}} \]

7. **Simplify the equation:**
\[ d = \frac{2 \times 1 \times 10^{-10} \times 2}{\sqrt{3}} \]
\[ d = \frac{4 \times 10^{-10}}{\sqrt{3}} \]

8. **Calculate the final value of \( d \):**
- Using \( \sqrt{3} \approx 1.732 \):
\[ d \approx \frac{4 \times 10^{-10}}{1.732} \approx 2.31 \times 10^{-10} \, \text{m} \]
- Converting to angstroms (1 Å = \( 10^{-10} \, \text{m} \)):
\[ d \approx 2.31 \, \text{Å} \]

### Final Answer:
The distance \( d \) for the second order diffraction is approximately \( 2.31 \, \text{Å} \).