50% of the X-ray coming from a Cooling tube is able to pass through a 0.1 mm thick aluminum foil. The potential difference between the target and the filament is increased. The thickness of aluminum foil, which will allow 50% of the X-ray to pass through, will be

Options

A. zero
B. `lt0.1 mm`
C. `0.1 mm`
D. `gt0.1 mm`

Answer

To solve the problem, we need to analyze the relationship between the thickness of the aluminum foil and the potential difference applied in the X-ray tube.

### Step-by-Step Solution:

1. **Understanding the Initial Condition**:
- We know that 50% of the X-rays can pass through a 0.1 mm thick aluminum foil. This means that the intensity of X-rays after passing through this thickness is half of the original intensity.

2. **Effect of Increasing Potential Difference**:
- When the potential difference between the target and the filament is increased, the energy of the X-rays produced also increases. Higher energy X-rays have greater penetrating power.

3. **Relationship Between Thickness and Penetrating Power**:
- The penetrating power of X-rays is inversely related to the wavelength (λ) of the X-rays. As the potential difference increases, the wavelength decreases, leading to an increase in penetrating power.

4. **Maintaining the Same Fraction of X-rays**:
- To maintain the same fraction of X-rays (50%) passing through the foil, we need to consider that with increased penetrating power, a thicker foil will be required to achieve the same attenuation (50% transmission).

5. **Conclusion**:
- Since the penetrating power of the X-rays has increased due to the higher potential difference, the thickness of the aluminum foil must also increase to maintain the same 50% transmission of X-rays. Therefore, the new thickness of the aluminum foil will be greater than 0.1 mm.

### Final Answer:
The thickness of the aluminum foil that will allow 50% of the X-rays to pass through will be greater than 0.1 mm.