On operating an X-ray tube at 1 kV. X-rays of minimum wavelength `6.22Å` are producd. I fht tube is operated at `10 kV`, then the minimum wavelength of `X`-rays prodcued will be

Options

A. `0.622Å`
B. `6.22Å`
C. `3.11 Å`
D. `62.2 Å`

Explanation

To solve the problem of finding the minimum wavelength of X-rays produced when the tube is operated at 10 kV, we can use the relationship between the wavelength of X-rays and the voltage applied in the X-ray tube. The wavelength is inversely proportional to the voltage.

### Step-by-Step Solution:

1. **Understand the relationship**: The minimum wavelength (λ) of X-rays produced in an X-ray tube is inversely proportional to the voltage (V) applied. This can be expressed mathematically as:
\[ \frac{\lambda_1}{\lambda_2} = \frac{V_2}{V_1} \]
where:
- \( \lambda_1 \) is the initial minimum wavelength,
- \( \lambda_2 \) is the new minimum wavelength,
- \( V_1 \) is the initial voltage,
- \( V_2 \) is the new voltage.

2. **Identify the known values**: From the problem, we know:
- \( \lambda_1 = 6.22 \, \text{Å} \)
- \( V_1 = 1 \, \text{kV} \)
- \( V_2 = 10 \, \text{kV} \)

3. **Set up the equation**: Plugging in the known values into the relationship gives:
\[ \frac{6.22 \, \text{Å}}{\lambda_2} = \frac{10 \, \text{kV}}{1 \, \text{kV}} \]

4. **Simplify the equation**: This simplifies to:
\[ \frac{6.22 \, \text{Å}}{\lambda_2} = 10 \]

5. **Solve for \( \lambda_2 \)**: Rearranging the equation to find \( \lambda_2 \):
\[ \lambda_2 = \frac{6.22 \, \text{Å}}{10} \]
\[ \lambda_2 = 0.622 \, \text{Å} \]

6. **Final answer**: The minimum wavelength of X-rays produced when the tube is operated at 10 kV is:
\[ \lambda_2 = 0.622 \, \text{Å} \]

### Conclusion:
Thus, the answer is \( 0.622 \, \text{Å} \).