If the X–ray tube is working at 25 kV then the minimum wavelength of X–rays will be

Options

A. 0.49 Å
B. 0.29 Å
C. 0.19 Å
D. 0.39 Å

Answer

To find the minimum wavelength of X-rays produced by an X-ray tube operating at a voltage of 25 kV, we can use the formula that relates the voltage (V) to the minimum wavelength (λ_min) of the emitted X-rays:

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

where:
- \(\lambda_{min}\) is in angstroms (Å),
- \(V\) is the voltage in kilovolts (kV).

### Step-by-step Solution:

1. **Convert the Voltage to Appropriate Units:**
The given voltage is 25 kV. We can keep it in kV since the formula uses kV directly.

2. **Substitute the Voltage into the Formula:**
Using the formula for minimum wavelength:
\[ \lambda_{min} = \frac{12375}{25} \]

3. **Calculate the Minimum Wavelength:**
Now, perform the calculation:
\[ \lambda_{min} = \frac{12375}{25} = 495 \text{ Å} \]

4. **Final Result:**
Therefore, the minimum wavelength of X-rays when the tube operates at 25 kV is:
\[ \lambda_{min} \approx 0.495 \text{ Å} \]

### Summary:
The minimum wavelength of X-rays produced by an X-ray tube operating at 25 kV is approximately 0.495 Å.

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