The kinetic energy of electrons that strike the target is increased , then the cut-off wavelength of continuous X-rays spectrum

Options

A. increases
B. decreases
C. no change
D. cannot be said

Answer

To solve the question regarding the effect of increasing the kinetic energy of electrons that strike the target on the cut-off wavelength of the continuous X-ray spectrum, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Concept of Cut-off Wavelength**:
The cut-off wavelength (\( \lambda_0 \)) in the context of X-ray production is defined as the maximum wavelength of the continuous X-ray spectrum. It is inversely related to the maximum energy of the electrons striking the target.

2. **Relating Kinetic Energy to Wavelength**:
The energy (\( E \)) of a photon is related to its wavelength (\( \lambda \)) by the equation:
\[ E = \frac{hc}{\lambda} \]
where \( h \) is Planck's constant and \( c \) is the speed of light. This implies that as the energy increases, the wavelength decreases.

3. **Effect of Increasing Kinetic Energy**:
When the kinetic energy of the electrons striking the target is increased, the energy of the emitted X-rays also increases. This is because the kinetic energy of the electrons is converted into X-ray photon energy when they decelerate upon hitting the target.

4. **Conclusion on Cut-off Wavelength**:
Since the energy of the emitted X-rays increases with the kinetic energy of the electrons, the cut-off wavelength will decrease. Therefore, if the kinetic energy of the electrons is increased, the cut-off wavelength of the continuous X-ray spectrum decreases.

5. **Final Answer**:
The correct option is that the cut-off wavelength decreases.

### Summary of Steps:
- Understand the relationship between energy and wavelength.
- Use the equation \( E = \frac{hc}{\lambda} \) to relate kinetic energy to cut-off wavelength.
- Conclude that increasing kinetic energy leads to a decrease in cut-off wavelength.