An X-ray tube is operated at 50 kV. The minimum wavelength produced is

Options

A. `0.5Å`
B. `0.5Å`
C. `0.25Å`
D. `1Å`

Explanation

To find the minimum wavelength produced by an X-ray tube operated at 50 kV, we can use the formula for the minimum wavelength (λ_min) in terms of the accelerating potential (V):

\[ \lambda_{\text{min}} = \frac{12375}{V} \]

### Step 1: Identify the given values
- The accelerating potential (V) is given as 50 kV.

### Step 2: Convert kV to volts
Since 1 kV = 1000 volts, we convert 50 kV to volts:
\[ V = 50 \, \text{kV} = 50 \times 10^3 \, \text{V} = 50000 \, \text{V} \]

### Step 3: Substitute the value of V into the formula
Now, we substitute the value of V into the formula for λ_min:
\[ \lambda_{\text{min}} = \frac{12375}{50000} \]

### Step 4: Perform the calculation
Calculating the above expression:
\[ \lambda_{\text{min}} = \frac{12375}{50000} = 0.2475 \, \text{Å} \]

### Step 5: Round the result
Rounding 0.2475 Å to two decimal places gives:
\[ \lambda_{\text{min}} \approx 0.25 \, \text{Å} \]

### Conclusion
The minimum wavelength produced by the X-ray tube is approximately 0.25 Å.

### Final Answer
The correct option is 0.25 Å.

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