Which one of the following statements is wrong in the context of X-ray generated from and X-ray tube?

Options

A. Wavelength of characterstics X-ray decreases when the atomic number of the target increases
B. Cut-off wavelength of the continuous X-rays depends on the atomic number of the target
C. Intensity of the characteristic X-rays depends on the elecreical power given to the X-ray tube
D. Cut-off wavelength of the continuous X-ray depends on the energy of the electrons in the X-ray tube

Explanation

To determine which statement is wrong in the context of X-ray generation from an X-ray tube, we will analyze each option provided in the question.

### Step-by-Step Solution:

1. **Understanding the Characteristics of X-rays**:
- X-rays are generated when high-energy electrons collide with a target material, typically made of a heavy metal like tungsten.

2. **Analyzing Statement 1**:
- **Statement**: "The wavelength of the characteristic X-ray decreases when the atomic number of the target increases."
- **Analysis**: The wavelength of characteristic X-rays is inversely proportional to the square of the atomic number (Z) of the target. This means that as Z increases, the wavelength decreases.
- **Conclusion**: This statement is **true**.

3. **Analyzing Statement 2**:
- **Statement**: "The cut-off wavelength of the continuous X-ray depends on the atomic number of the target."
- **Analysis**: The cut-off wavelength (λ) for continuous X-rays is given by the formula:
\[ \lambda = \frac{hc}{eV} \]
where \( h \) is Planck's constant, \( c \) is the speed of light, \( e \) is the charge of an electron, and \( V \) is the accelerating voltage. This formula shows that the cut-off wavelength depends on the energy of the electrons (related to the voltage) and not on the atomic number of the target.
- **Conclusion**: This statement is **false** (wrong).

4. **Analyzing Statement 3**:
- **Statement**: "The intensity of characteristic X-ray depends on the electrical power given to the X-ray tube."
- **Analysis**: The intensity of characteristic X-rays is indeed related to the power supplied to the X-ray tube, as higher power means more electrons are available for collision with the target, resulting in more X-rays being produced.
- **Conclusion**: This statement is **true**.

5. **Analyzing Statement 4**:
- **Statement**: "The cut-off wavelength of the continuous X-ray depends on the energy of the electron in the X-ray tube."
- **Analysis**: As mentioned in the analysis of statement 2, the cut-off wavelength is inversely proportional to the energy of the electrons (which is related to the voltage). Therefore, this statement is correct.
- **Conclusion**: This statement is **true**.

### Final Conclusion:
After analyzing all statements, the wrong statement in the context of X-ray generation from an X-ray tube is **Statement 2**.