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Assertion: Angular momentum of single el...

Assertion: Angular momentum of single electron in any orbit or hydrogen type atom is independent of the atomic number of the element.
Reason: In ground state angular momentum is minimum

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 given question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that the angular momentum of a single electron in any orbit of a hydrogen-type atom is independent of the atomic number of the element. - The formula for angular momentum (L) of an electron in orbit is given by: \[ L = n \frac{h}{2\pi} \] where \( n \) is the principal quantum number and \( h \) is Planck's constant. 2. **Analyzing the Angular Momentum**: - From the formula, we can see that the angular momentum depends only on the principal quantum number \( n \) and not on the atomic number \( Z \) of the atom. - Therefore, the assertion is **true**. 3. **Understanding the Reason**: - The reason states that in the ground state, the angular momentum is minimum. - The ground state corresponds to \( n = 1 \), which gives: \[ L = 1 \cdot \frac{h}{2\pi} = \frac{h}{2\pi} \] - This is indeed the minimum value of angular momentum for any electron in a hydrogen-like atom. 4. **Evaluating the Relationship**: - While both the assertion and the reason are true, the reason does not explain why the angular momentum is independent of the atomic number. - The reason merely states a fact about the ground state without linking it back to the assertion. 5. **Conclusion**: - Since both the assertion and the reason are true, but the reason does not serve as an explanation for the assertion, the correct answer is that both are true but the reason is not the correct explanation of the assertion. ### Final Answer: The correct option is **B**: Both assertion and reason are true, but reason is not the correct explanation of assertion.

To solve the given question, we need to analyze both the assertion and the reason provided. ### Step-by-Step Solution: 1. **Understanding the Assertion**: - The assertion states that the angular momentum of a single electron in any orbit of a hydrogen-type atom is independent of the atomic number of the element. - The formula for angular momentum (L) of an electron in orbit is given by: \[ ...
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