The argentite or silver glance is $$A{g_2}S,$$  it is an ore of silver. Haematite $$F{e_2}{O_3}$$  is ore of iron, bauxite is ore of aluminium whereas stibnite $$S{b_2}{S_3}$$  sometimes stibnite called antimonite is an ore of antimony.

$$4f$$ orbital is nearer to nucleus as compared to $$5f$$ orbital therefore, shielding of $$4f$$ is more than $$5f.$$

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$$Ce$$  is most commonly used lanthanide, nobelium $$(No)$$  and $$Th$$  (thorium) are actinides.

$$2KMn{O_4} + 2{H_2}S{O_4}\left( {conc.} \right) \to $$      $$\mathop {M{n_2}{O_7}}\limits_{{\text{(green oily)}}} + 2KHS{O_4} + {H_2}O$$

$$\mu = \sqrt {n\left( {n + 2} \right)} \,B.M.$$

Manganese is responsible for oxidation of water to $${O_2}$$  in biological processes.

$$5{C_2}O_4^{2 - } + \mathop {2MnO_4^ - }\limits_{{\text{(coloured}})} + 16{H^ + }$$     $$ \to \mathop {2M{n^{2 + }}}\limits_{{\text{(colourless)}}} + 8{H_2}O + 10C{O_2}$$

Positive $${E^ \circ }$$ value of copper accounts for its inability to liberate $${H_2}$$  from acids.

All actinides show different oxidation states such as +2 +3 +4 +5 and +7. However, +3 oxidation state is most common among all the actinides. The wide range of oxidation states of actinides is attributed to the fact that the $$5f, 6d$$   and $$7s$$  energy levels are of comparable energies. Therefore, all these three sub-shells can participate.