Assertion: If applied potential difference in coolidge tube is increased, then difference in coolidge tube.

Options

A. If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.
B. If both Assertion and Reason or true but Reason is not the correct explanation of Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion is false but the Reason is true.

Explanation

To solve the question regarding the assertion about the Coolidge tube, let's break it down step by step:

### Step 1: Understanding the Coolidge Tube
The Coolidge tube is a type of X-ray tube where electrons are accelerated towards a target by a high voltage. When these high-energy electrons collide with the target, they produce X-rays.

**Hint:** Familiarize yourself with the basic functioning of the Coolidge tube and how it generates X-rays.

### Step 2: Cut-off Wavelength
The cut-off wavelength (λ_min) is the minimum wavelength of the X-rays produced, which is determined by the energy of the electrons hitting the target. The relationship is given by the formula:
\[ \lambda_{\text{min}} = \frac{hc}{eV} \]
where:
- \( h \) is Planck's constant,
- \( c \) is the speed of light,
- \( e \) is the charge of an electron,
- \( V \) is the applied potential difference.

**Hint:** Recall the relationship between energy and wavelength in the context of X-ray production.

### Step 3: Inverse Relationship
From the formula, we can see that the cut-off wavelength is inversely proportional to the applied potential difference (V). As the potential difference increases, the cut-off wavelength decreases:
\[ \lambda_{\text{min}} \propto \frac{1}{V} \]

**Hint:** Understand how changes in voltage affect the energy of the electrons and consequently the wavelength of the emitted X-rays.

### Step 4: Difference in Wavelengths
The assertion states that if the applied potential difference is increased, the difference between the K-alpha wavelength and the cut-off wavelength will increase. The K-alpha wavelength is a specific wavelength associated with a characteristic X-ray transition.

**Hint:** Consider how the K-alpha wavelength relates to the cut-off wavelength and how changes in the cut-off wavelength affect their difference.

### Step 5: Analyzing the Assertion
If the potential difference (V) is increased:
- The cut-off wavelength (λ_min) decreases.
- The difference between the K-alpha wavelength and the cut-off wavelength (Δλ) can be expressed as:
\[ \Delta \lambda = \lambda_{K\alpha} - \lambda_{\text{min}} \]

As λ_min decreases (due to increased V), Δλ increases if λ_Kα remains constant.

**Hint:** Think about how the relationship between the cut-off wavelength and the K-alpha wavelength changes with varying potential differences.

### Step 6: Conclusion
Both the assertion and the reason are true:
- The assertion is that increasing the potential difference increases the difference between the K-alpha wavelength and the cut-off wavelength.
- The reason provided explains the relationship between the cut-off wavelength and the applied potential difference.

However, the reason does not directly explain the assertion, as it focuses only on the cut-off wavelength without addressing the K-alpha wavelength.

**Hint:** Differentiate between the assertion and the reason to see if they are logically connected.

### Final Answer
Both the assertion and the reason are true, but the reason is not the correct explanation for the assertion.