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Assertion: Wavelength of characteristic ...

Assertion: Wavelength of characteristic X-rays is given by
`(1)/(lambda)prop((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
in the transition from `n_(2) to n_(1)` . In the above relation propotionally constant does not deped upon the traget material.
Reason :Continuous X-rays are target independent.

A

If both Assertion and Reason ar true and Reason is the correct explanation of Assertion.

B

If both Assertion and Reason are true but Reason is not correct explanation of Assertion

C

If Assertion is true by Reason is false.

D

If Assertion is false but Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we will analyze the assertion and the reason provided, and then determine their validity and relationship. ### Step 1: Analyze the Assertion The assertion states that the wavelength of characteristic X-rays is given by the formula: \[ \frac{1}{\lambda} \propto \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) \] where \( n_1 \) and \( n_2 \) are principal quantum numbers corresponding to the energy levels involved in the transition. The assertion also claims that the proportionality constant does not depend on the target material. ### Step 2: Understanding the Proportionality Constant In the context of X-ray production, the proportionality constant can be expressed as: \[ \text{Proportionality Constant} \propto (Z - B)^2 \] where \( Z \) is the atomic number of the target material and \( B \) is a constant related to the material. This indicates that while the formula itself is valid for any target material, the specific value of the proportionality constant does depend on the target material. Therefore, the assertion that the proportionality constant does not depend on the target material is **false**. ### Step 3: Analyze the Reason The reason states that continuous X-rays are target independent. Continuous X-rays (or Bremsstrahlung radiation) are produced when high-energy electrons are decelerated upon interaction with the target material. This process does not depend on the specific type of target material, as it is a general phenomenon that occurs with any target. Thus, the reason is **true**. ### Step 4: Conclusion Now we can summarize our findings: - The assertion is **false** because the proportionality constant does depend on the target material. - The reason is **true** because continuous X-rays are indeed target independent. ### Final Answer Both assertion and reason are not true in relation to each other. The correct option would be that the assertion is false, while the reason is true.

To solve the question, we will analyze the assertion and the reason provided, and then determine their validity and relationship. ### Step 1: Analyze the Assertion The assertion states that the wavelength of characteristic X-rays is given by the formula: \[ \frac{1}{\lambda} \propto \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) \] where \( n_1 \) and \( n_2 \) are principal quantum numbers corresponding to the energy levels involved in the transition. ...
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