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Mendeleev predicted the existence of certain elements not known at that time and named two of them as Eka — silicon and Eka — Aluminium.
Mention the group of these elements in the Modern Periodic Table:
A) Group 12 and Group 13
B) Group 14 and Group 15
C) Group 14 and Group 13
D) Group 15 and Group 13

Answer
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Hint: Mendeleev proposed a periodic table model based on atomic mass. He clubbed all elements which have similar properties and arranged them according to increasing atomic weight. The eka elements were later discovered. The term ‘eka –element’ is used to represent those elements which have not yet been discovered.

Complete step by step answer:
Dmitri Ivanovich Mendeleev proposed an early model of the periodic table. Mendeleev arranged elements according to the chemical properties of the elements. He grouped the elements according to their similarities in properties. He arranged all elements as increasing order of atomic mass and their similar properties.
Mendeleev leaves some gaps in the periodic table. This gap corresponds to the element which lies in a periodic table. He named these undiscovered elements as Eka silicon and Eka aluminium. Later on, in the modern periodic table, the eka silicon is germanium .it has similar properties as that of silicon.
Eka aluminium is gallium. It has similar properties as that of aluminium.
The gallium has an electronic configuration as follows,
$\text{ Ga= Ar 3}{{\text{d}}^{\text{10}}}\text{4}{{\text{s}}^{\text{2}}}\text{4}{{\text{p}}^{\text{1}}}\text{ }$
It has valence shell configuration as $\text{ n}{{\text{s}}^{\text{2}}}\text{n}{{\text{p}}^{\text{1}}}\text{ }$. Group 13 elements have three valence electrons. It is a fourth-period element as the outermost shell number is 4. Thus, aluminium is gallium and it is a group of 13 elements.
The germanium has an electronic configuration as follows,
$\text{ Ga= Ar 3}{{\text{d}}^{\text{10}}}\text{4}{{\text{s}}^{\text{2}}}\text{4}{{\text{p}}^{2}}\text{ }$
It has valence shell configuration as $\text{ n}{{\text{s}}^{\text{2}}}\text{n}{{\text{p}}^{2}}\text{ }$ .group 14 elements have four valence electron. It is a fourth-period element as the outermost shell number is 4. Thus, silicon is germanium and it is a group of 14 elements.
Thus eka-silicon and eka-aluminium are group 14 and group 13 elements.

Hence, (C) is the correct option.

Note: Note that, few more elements remained as a gap Mendeleev periodic table. Mendeleev also predicted the existence of the elements of the analogue of manganese, tellurium, iodine, barium. Some other elements were discovered later such as eka boron, scandium.