If the potential difference applied across a Coolidge tube is increased , then

Options

A. wavelength of `K_(alpha)` will increase
B. `lambda_(min)` will increase
C. different between wavelength of `K_(alpha)` and `lambda_(min)` increase
D. none of these

Explanation

To solve the question regarding the effect of increasing the potential difference across a Coolidge tube, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Coolidge Tube**:
- A Coolidge tube is a type of X-ray tube where electrons are accelerated towards a target (anode) by a high voltage (potential difference). When these high-energy electrons collide with the anode, they produce X-rays.

2. **Effect of Increasing Potential Difference**:
- When the potential difference (V) across the Coolidge tube is increased, the kinetic energy of the electrons striking the anode also increases. The kinetic energy (KE) of the electrons can be expressed as:
\[ KE = eV \]
where \( e \) is the charge of the electron and \( V \) is the potential difference.

3. **Energy of Emitted X-rays**:
- The energy of the emitted X-rays is directly related to the kinetic energy of the electrons. Therefore, as the potential difference increases, the energy of the emitted X-rays also increases.

4. **Wavelength of X-rays**:
- The energy of a photon (X-ray) 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. As the energy \( E \) increases, the wavelength \( \lambda \) decreases.

5. **K-alpha Wavelength and Minimum Wavelength**:
- The K-alpha line refers to a specific wavelength of X-ray emitted when an electron transitions to the K-shell from a higher energy level. The minimum wavelength (\( \lambda_{\text{min}} \)) corresponds to the maximum energy of the X-rays produced, which is determined by the maximum kinetic energy of the electrons.
- As the potential difference increases, both the K-alpha wavelength and the minimum wavelength will decrease, but the difference between them will increase.

6. **Conclusion**:
- Therefore, the correct conclusion is that the difference between the wavelength of K-alpha and the minimum wavelength increases. Thus, the correct option is:
- **Option C: The difference between the wavelength of K-alpha and the minimum wavelength increases.**