The borax bead test is a qualitative chemical test used to detect the presence of certain metal ions. It works by reacting metal salts with borax $ Na_2B_4O_7 \cdot 10H_2O $, which on heating forms a glassy bead containing metal borates. The color of the bead is characteristic of the metal ion present.
Hot bead colors for the following transition metal ions:
Manganese(II) ions (Mn²⁺) produce a violet-colored bead in the borax bead test. Additionally, Mn²⁺ has a d⁵ electronic configuration, which is relatively stable and less influenced by the surrounding ligand field, making it a distinctive case.
Electronic configurations:
Among the given options, $ Mn^{2+} $ matches both the observed color and the electronic configuration.
Final Answer:
The final answer is $ Mn^{2+} $.
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: