The penetration power of `X`-ray increases with the increases in its:

Options

A. Accelerating potential
B. Wavelength
C. Mass number of the target material
D. Filament current

Answer

To solve the question regarding the penetration power of X-rays and how it increases, we can follow these steps:

### Step 1: Understand the relationship between energy and penetration power
The penetration power of X-rays is directly related to their energy. Higher energy X-rays can penetrate materials more effectively than lower energy X-rays.

**Hint:** Recall that higher energy photons can overcome the binding energy of electrons in materials more easily.

### Step 2: Relate energy to wavelength
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,
- \( \lambda \) is the wavelength.

From this formula, we can see that as the wavelength (\( \lambda \)) decreases, the energy (\( E \)) increases.

**Hint:** Remember that shorter wavelengths correspond to higher energy in electromagnetic radiation.

### Step 3: Consider the effect of accelerating potential
The energy of X-rays produced in an X-ray tube is also related to the accelerating potential (V) applied to the electrons. The energy gained by the electrons when they are accelerated through a potential difference is given by:
\[ E = eV \]
where:
- \( e \) is the charge of the electron,
- \( V \) is the accelerating potential.

As the accelerating potential increases, the energy of the X-rays also increases.

**Hint:** Think about how increasing the voltage in an X-ray tube affects the energy of the emitted X-rays.

### Step 4: Analyze the options given in the question
1. **Accelerating potential**: As discussed, increasing the accelerating potential increases the energy of the X-rays, thus increasing their penetration power. This option is correct.
2. **Wavelength**: Increasing the wavelength would decrease the energy of the X-rays, which would decrease their penetration power. This option is incorrect.
3. **Mass number of the target material**: The penetration power of X-rays is not dependent on the mass number of the target material. This option is incorrect.
4. **Filament current**: While filament current affects the quantity of X-rays produced, it does not directly affect their energy or penetration power. This option is incorrect.

### Conclusion
Based on the analysis, the correct answer is that the penetration power of X-rays increases with an increase in their **accelerating potential**.

**Final Answer:** The penetration power of X-rays increases with the increase in its **accelerating potential**.