List-I (Complex ion) | List-II (Spin only magnetic moment in B.M.) |
---|---|
(A) [Cr(NH$_3$)$_6$]$^{3+}$ | (I) 4.90 |
(B) [NiCl$_4$]$^{2-}$ | (II) 3.87 |
(C) [CoF$_6$]$^{3-}$ | (III) 0.0 |
(D) [Ni(CN)$_4$]$^{2-}$ | (IV) 2.83 |
The spin-only magnetic moment ($\mu$) in Bohr Magnetons (B.M.) is calculated using the formula: \[ \mu = \sqrt{n(n+2)} \, \text{B.M.}, \] where $n$ is the number of unpaired electrons.
(A) [Cr(NH$_3$)$_6$]$^{3+}$: \[ \text{Cr}^{3+}: 3d^3 \, (3 \, \text{unpaired electrons}). \]
\[ \mu = \sqrt{3(3+2)} = 3.87 \, \text{B.M.} \, (\text{II}). \]
(B) [NiCl$_4$]$^{2-}$: \[ \text{Ni}^{2+}: 3d^8 \, (2 \, \text{unpaired electrons}). \]
\[ \mu = \sqrt{2(2+2)} = 2.83 \, \text{B.M.} \, (\text{IV}). \]
(C) [CoF$_6$]$^{3-}$: \[ \text{Co}^{3+}: 3d^6 \, (4 \, \text{unpaired electrons}). \]
\[ \mu = \sqrt{4(4+2)} = 4.90 \, \text{B.M.} \, (\text{I}). \]
(D) [Ni(CN)$_4$]$^{2-}$: \[ \text{Ni}^{2+}: 3d^8 \, (\text{low spin, 0 unpaired electrons}). \]
\[ \mu = \sqrt{0(0+2)} = 0.0 \, \text{B.M.} \, (\text{III}). \]
The correct matching is: \[ \text{(A)-(II), (B)-(IV), (C)-(I), (D)-(III)}. \]
Match the following List-I with List-II and choose the correct option: List-I (Compounds) | List-II (Shape and Hybridisation) (A) PF\(_{3}\) (I) Tetrahedral and sp\(^3\) (B) SF\(_{6}\) (III) Octahedral and sp\(^3\)d\(^2\) (C) Ni(CO)\(_{4}\) (I) Tetrahedral and sp\(^3\) (D) [PtCl\(_{4}\)]\(^{2-}\) (II) Square planar and dsp\(^2\)
Let \( y = f(x) \) be the solution of the differential equation
\[ \frac{dy}{dx} + 3y \tan^2 x + 3y = \sec^2 x \]
such that \( f(0) = \frac{e^3}{3} + 1 \), then \( f\left( \frac{\pi}{4} \right) \) is equal to:
Find the IUPAC name of the compound.
If \( \lim_{x \to 0} \left( \frac{\tan x}{x} \right)^{\frac{1}{x^2}} = p \), then \( 96 \ln p \) is: 32