Vanadium (V) has the highest enthalpy of atomisation (515 kJ/mol) among first-row transition elements. When it forms an oxide, it produces \( \text{V}_2\text{O}_5 \).
In \( \text{V}_2\text{O}_5 \):
Vanadium is in the \( +5 \) oxidation state.
The electron configuration of \( \text{V}^{5+} \) is \( 1s^2 2s^2 2p^6 3s^2 3p^6 \), with no unpaired electrons.
Since there are no unpaired electrons in \( \text{V}^{5+} \), the "spin-only" magnetic moment is zero.
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: