Penetrating power of X-rays increase with the increase in its

Options

A. intensity
B. amplitude
C. frequency
D. wavelength

Answer

To solve the question regarding the penetrating power of X-rays, we need to analyze how it relates to various properties of X-rays, particularly energy and frequency.

### Step-by-Step Solution:

1. **Understanding Penetrating Power**:
- The penetrating power of X-rays refers to their ability to pass through materials. Higher penetrating power means that X-rays can pass through denser materials without being absorbed.

2. **Energy of X-rays**:
- The energy (E) of X-rays can be expressed using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \(E\) is the energy,
- \(h\) is Planck's constant,
- \(c\) is the speed of light, and
- \(\lambda\) is the wavelength of the X-ray.

3. **Relationship Between Wavelength and Frequency**:
- The wavelength (\(\lambda\)) and frequency (\(\nu\)) of X-rays are related by the equation:
\[ \lambda = \frac{c}{\nu} \]
- Rearranging this gives:
\[ \nu = \frac{c}{\lambda} \]

4. **Substituting Wavelength in Energy Equation**:
- By substituting \(\lambda\) in the energy equation, we can rewrite the energy in terms of frequency:
\[ E = h\nu \]
- This shows that energy is directly proportional to frequency.

5. **Increasing Frequency**:
- From the equation \(E = h\nu\), we see that as frequency (\(\nu\)) increases, the energy (E) of the X-rays also increases.

6. **Penetrating Power and Energy**:
- It is known that the penetrating power of X-rays increases with an increase in energy. Therefore, since energy increases with frequency, we conclude that:
- The penetrating power of X-rays increases with an increase in frequency.

7. **Final Answer**:
- Thus, the correct option is that the penetrating power of X-rays increases with the increase in its **frequency**.

### Conclusion:
The correct answer is that the penetrating power of X-rays increases with the increase in its **frequency**.

---