The electronic configurations and the number of unpaired electrons for each element are as follows:
Sc: \([ \text{Ar} ] 4s^2 3d^1 \quad (1 \text{ unpaired electron})\)
Cr: \([ \text{Ar} ] 4s^1 3d^5 \quad (6 \text{ unpaired electrons})\)
V: \([ \text{Ar} ] 4s^2 3d^3 \quad (3 \text{ unpaired electrons})\)
Ti: \([ \text{Ar} ] 4s^2 3d^2 \quad (2 \text{ unpaired electrons})\)
Mn: \([ \text{Ar} ] 4s^2 3d^5 \quad (5 \text{ unpaired electrons})\)
Arranging them in increasing order of unpaired electrons, we get:
\(\text{Sc (A)} < \text{Ti (D)} < \text{V (C)} < \text{Mn (E)} < \text{Cr (B)}\)
List-I ( Ions ) | List-II ( No. of unpaired electrons ) | ||
A | Zn$^{2+}$ | (I) | 0 |
B | Cu$^{2+}$ | (II) | 4 |
C | Ni$^{2+}$ | (III) | 1 |
D | Fe$^{2+}$ | (IV) | 2 |
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: