If the potential difference of coolidge tube probucing X-ray is increased, then choose the corrent option (s).
Here, `lambda_0` is cut off wavelength and `lambda_(Ka) and lambda_(K beta)` are wavelengths of `K_(alpha) and K_(beta)` characteristic X-rays.

Options

A. the interval between `lambda_(Kalpha)` and `lambda_(Kbeta) ` increases
B. the interval between `lambda_(Kalpha)` and `lambda_0 ` increases
C. the interval between `lambda_(Kbeta)` and `lambda_0 ` increases
D. `lambda_0` does not change

Explanation

To solve the problem, we need to analyze how the increase in potential difference (V) in a Coolidge tube affects the wavelengths of the emitted X-rays, specifically the cut-off wavelength (λ₀) and the characteristic wavelengths (λₖₐ and λₖβ).

### Step-by-Step Solution:

1. **Understanding the Cut-off Wavelength (λ₀)**:
The cut-off wavelength (λ₀) is given by the formula:
\[ λ₀ = \frac{hc}{eV} \]
where:
- \(h\) is Planck's constant,
- \(c\) is the speed of light,
- \(e\) is the charge of an electron,
- \(V\) is the potential difference.

2. **Effect of Increasing Potential Difference (V)**:
From the formula, we can see that λ₀ is inversely proportional to the potential difference (V). This means:
- If \(V\) increases, then \(λ₀\) decreases.

3. **Analyzing the Wavelengths of Characteristic X-rays**:
The characteristic X-ray wavelengths (λₖₐ and λₖβ) are specific to the material and are not directly affected by the potential difference. However, the intervals between these wavelengths and λ₀ will change as λ₀ changes.

4. **Interval Between Wavelengths**:
- The interval between λₖₐ and λ₀ is given by:
\[ \text{Interval}_{kα} = λₖₐ - λ₀ \]
Since λ₀ decreases, this interval increases.

- The interval between λₖβ and λ₀ is given by:
\[ \text{Interval}_{kβ} = λₖβ - λ₀ \]
Similarly, since λ₀ decreases, this interval also increases.

5. **Conclusion**:
- The interval between λₖₐ and λₖβ does not change because the characteristic wavelengths are fixed for a given material.
- The intervals between λₖₐ and λ₀, and λₖβ and λ₀ both increase due to the decrease in λ₀.

### Correct Options:
- The interval between λₖₐ and λ₀ increases (Correct).
- The interval between λₖβ and λ₀ increases (Correct).
- The interval between λₖₐ and λₖβ does not change (Incorrect).
- λ₀ does change (Incorrect).

### Final Answer:
The correct options are:
- The interval between λₖₐ and λ₀ increases.
- The interval between λₖβ and λ₀ increases.