If vacuum tube is operated at 6.4 kV, what is the wavelength of X-ray produced :-

Options

A. 1.93Å
B. 1.53Å
C. 2.67Å
D. 0.78Å

Answer

To find the wavelength of X-rays produced when a vacuum tube is operated at a potential difference of 6.4 kV, we can use the formula that relates the wavelength of X-rays to the potential difference. The formula is given by:

\[ \lambda = \frac{12375}{V} \]

where:
- \(\lambda\) is the wavelength in angstroms (Å),
- \(V\) is the potential difference in volts (V).

### Step-by-Step Solution:

1. **Convert the potential difference from kilovolts to volts:**
\[ V = 6.4 \, \text{kV} = 6.4 \times 10^3 \, \text{V} = 6400 \, \text{V} \]

2. **Substitute the value of \(V\) into the wavelength formula:**
\[ \lambda = \frac{12375}{6400} \]

3. **Calculate the wavelength:**
\[ \lambda = \frac{12375}{6400} \approx 1.9328125 \, \text{Å} \]

4. **Round the result to three significant figures:**
\[ \lambda \approx 1.93 \, \text{Å} \]

### Final Answer:
The wavelength of the X-ray produced is approximately **1.93 Å**.

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