List-I | List-II |
---|---|
(A) Mn2+ | (I) Pyrolusite ore |
(B) Spin only Magnetic Moment | (II) An alloy of 4f metal, iron and traces of S, C, Al and Ca |
(C) MnO2 | (III) μs = √n(n + 2) BM |
(D) Misch metal | (IV) Highest oxidation states |
To match the elements in List-I with the correct descriptions in List-II, we must understand the properties and associations of the given elements and terms. Here is the detailed analysis and reasoning:
Conclusion: Based on the above analysis, the correct match is: (A)- (IV), (B)- (III), (C)- (I), (D)- (II)
(A) Mn²⁺: Manganese in the +2 oxidation state \(({Mn}^{2+})\)is associated with the highest oxidation states of manganese, specifically in the context of its other oxidation states. Therefore, it matches with (IV).
(B) Spin-only magnetic moment: The formula for the spin-only magnetic moment is given by \(\mu_s = \sqrt{n(n+2)}\), where n is the number of unpaired electrons. This matches with (III).
(C) MnO₂: Manganese dioxide \(({MnO_2})\) is also known as pyrolusite ore, which is the primary source of manganese. Therefore, it matches with (I).
(D) Misch metal: Misch metal is an alloy of 4f metals (lanthanides), iron, and small amounts of sulfur, carbon, aluminum, and calcium. This matches with (II).
Therefore, the correct answer is Option C.
(b) If \( \vec{L} \) is the angular momentum of the electron, show that:
\[ \vec{\mu} = -\frac{e}{2m} \vec{L} \]
The sum of the spin-only magnetic moment values (in B.M.) of $[\text{Mn}(\text{Br})_6]^{3-}$ and $[\text{Mn}(\text{CN})_6]^{3-}$ is ____.