LIST-I | LIST-II | ||
---|---|---|---|
I | \(\text{[Cr(CN)}_6\text{]}^{4-}\) | P | t2g orbitals contain 4 electrons |
II | \(\text{[RuCl}_6\text{]}^{2-}\) | Q | \(\mu\)(spin-only) = 4.9 BM |
III | \(\text{[Cr(H}_2\text{O)}_6\text{]}^{2+}\) | R | low spin complex ion |
IV | \(\text{[Fe(H}_2\text{O)}_6\text{]}^{2+}\) | S | metal ion in 4+ oxidation state |
T | d4 species |
I → R, T; II → P, S; III → Q, T; IV → P, Q
I → R, S; II → P, T; III → P, Q; IV → Q, T
I → P, R; II → R, S; III → R, T; IV → P, T
I → Q, T; II → S, T; III → P, T; IV → Q, R
(I) \(\text{[Cr(CN)}_6\text{]}^{4-}\)
The Cr2+ ion, with the electron configuration [Ar] 3d4 4s0, undergoes d2sp3 hybridization due to the strong field ligand CN–.
(II) \(\text{[RuCl}_6\text{]}^{2-}\):
The Ru4+ ion, with the electron configuration [Kr] 4d4 5s0, has a t2g set that contains four electrons.
(III) \(\text{[Cr(H}_2\text{O)}_6\text{]}^{2+}\):
The Cr2+ ion, with the electron configuration [Ar] 3d4 4s0, exhibits four unpaired electrons due to the weak field ligand H2O, resulting in a magnetic moment of 4.9 B.M.
(IV) \(\text{[Fe(H}_2\text{O)}_6\text{]}^{2+}\)
The Fe2+ ion, with the electron configuration [Ar] 3d6 4s0, also possesses four unpaired electrons, resulting in a magnetic moment of 4.9 B.M.
Hence option A is Correct
In the following species, how many species have the same magnetic moment?
(i) Cr\(^{2+}\)
(ii) Mn\(^{3+}\)
(iii) Ni\(^{2+}\)
(iv) Sc\(^{2+}\)
(v) Zn\(^{2+}\)
(vi) V\(^{3+}\)
(vii) Ti\(^{4+}\)
A temperature difference can generate e.m.f. in some materials. Let $ S $ be the e.m.f. produced per unit temperature difference between the ends of a wire, $ \sigma $ the electrical conductivity and $ \kappa $ the thermal conductivity of the material of the wire. Taking $ M, L, T, I $ and $ K $ as dimensions of mass, length, time, current and temperature, respectively, the dimensional formula of the quantity $ Z = \frac{S^2 \sigma}{\kappa} $ is:
Let $ a_0, a_1, ..., a_{23} $ be real numbers such that $$ \left(1 + \frac{2}{5}x \right)^{23} = \sum_{i=0}^{23} a_i x^i $$ for every real number $ x $. Let $ a_r $ be the largest among the numbers $ a_j $ for $ 0 \leq j \leq 23 $. Then the value of $ r $ is ________.
Let $ y(x) $ be the solution of the differential equation $$ x^2 \frac{dy}{dx} + xy = x^2 + y^2, \quad x > \frac{1}{e}, $$ satisfying $ y(1) = 0 $. Then the value of $ 2 \cdot \frac{(y(e))^2}{y(e^2)} $ is ________.