An X-ray tube is operated at 20 kV. The cut off wavelength is

Options

A. `0.89 Å`
B. `0.75 Å`
C. `0.62 Å`
D. None of these

Explanation

To find the cut-off wavelength of an X-ray tube operated at 20 kV, we can use the formula for the minimum wavelength (cut-off wavelength) given by:

\[ \lambda_{\text{min}} = \frac{12423}{V} \]

where:
- \(\lambda_{\text{min}}\) is the cut-off wavelength in angstroms (Å),
- \(V\) is the operating voltage in volts.

### Step-by-step Solution:

1. **Identify the Voltage**:
The X-ray tube is operated at 20 kV. We need to convert this to volts:
\[ V = 20 \text{ kV} = 20 \times 10^3 \text{ V} = 20000 \text{ V} \]

2. **Substitute the Voltage into the Formula**:
Now we will substitute the value of \(V\) into the cut-off wavelength formula:
\[ \lambda_{\text{min}} = \frac{12423}{20000} \]

3. **Perform the Calculation**:
Now we calculate the value:
\[ \lambda_{\text{min}} = \frac{12423}{20000} = 0.62115 \text{ Å} \]

4. **Round the Result**:
Rounding this value to two decimal places, we get:
\[ \lambda_{\text{min}} \approx 0.62 \text{ Å} \]

5. **Select the Correct Option**:
Now, we check the options provided:
- Option 1: 0.89 Å
- Option 2: 0.75 Å
- Option 3: 0.62 Å
- Option 4: None of these

The correct answer is **Option 3: 0.62 Å**.

### Summary:
The cut-off wavelength for an X-ray tube operated at 20 kV is approximately **0.62 Å**.