Match List - I with List - II:
List - I:
(A) \([ \text{MnBr}_4]^{2-}\)
(B) \([ \text{FeF}_6]^{3-}\)
(C) \([ \text{Co(C}_2\text{O}_4)_3]^{3-}\)
(D) \([ \text{Ni(CO)}_4]\)
List - II:
(I) d²sp³ diamagnetic
(II) sp²d² paramagnetic
(III) sp³ diamagnetic
(IV) sp³ paramagnetic
To solve the problem of matching List-I with List-II, we need to determine the hybridization of each complex and their magnetic properties:
Thus, the correct matches are:
| List-I | List-II |
|---|---|
| (A) \([ \text{MnBr}_4]^{2-}\) | (III) sp³ diamagnetic |
| (B) \([ \text{FeF}_6]^{3-}\) | (II) sp²d² paramagnetic |
| (C) \([ \text{Co(C}_2\text{O}_4)_3]^{3-}\) | (I) d²sp³ diamagnetic |
| (D) \([ \text{Ni(CO)}_4]\) | (IV) sp³ paramagnetic |
The correct answer is:
(A)-(III),(B)-(II),(C)-(I),(D)-(IV)
Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.