An X-ray tube with Cu target is operated at 25 kV. The glancing angle for a NaCl. Crystal for the Cu`k_alpha` line is `15.8^@` . Find the wavelength of this line.

Options

A. 3.06Å
B. 1.53Å
C. 0.75 Å
D. none of these

Explanation

To find the wavelength of the Cu K_alpha line using Bragg's law, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Bragg's Law**:
Bragg's law relates the wavelength of X-rays to the angle of diffraction and the spacing between crystal planes. The formula is given by:
\[ 2d \sin \theta = n \lambda \]
where:
- \(d\) = distance between crystal planes,
- \(\theta\) = glancing angle,
- \(n\) = order of diffraction (for the first order, \(n = 1\)),
- \(\lambda\) = wavelength of the X-ray.

2. **Identifying Given Values**:
- The glancing angle \(\theta = 15.8^\circ\).
- The distance between crystal planes for NaCl, \(d = 2.82 \, \text{Å}\) (angstroms).
- We will use \(n = 1\) for the first order diffraction.

3. **Substituting Values into Bragg's Law**:
We can now substitute the known values into Bragg's law:
\[ 2d \sin \theta = \lambda \]
Substituting \(d\) and \(\theta\):
\[ 2 \times 2.82 \times \sin(15.8^\circ) = \lambda \]

4. **Calculating \(\sin(15.8^\circ)\)**:
Using a calculator, we find:
\[ \sin(15.8^\circ) \approx 0.272 \]

5. **Calculating the Wavelength \(\lambda\)**:
Now we can calculate \(\lambda\):
\[ \lambda = 2 \times 2.82 \times 0.272 \]
\[ \lambda = 2 \times 2.82 \times 0.272 \approx 1.53 \, \text{Å} \]

6. **Final Result**:
The wavelength of the Cu K_alpha line is approximately \(1.53 \, \text{Å}\).

### Conclusion:
The correct answer is \(B. 1.53 \, \text{Å}\).