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In any short period the valency of an element with respect to oxygen
(A) Increases one by one from \[I\]A to \[VII\]A
(B) Decreases one by one from \[I\]A to \[VII\]A
(C) Increases one by one from \[I\]A to \[IV\]A and then decreases from \[V\]A to \[VII\]A one by one
(D) Decreases one by one from \[I\]A to \[IV\]A and then Increases from \[V\]A to \[VII\]A one by one

Answer
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Hint: On moving from left to right in a period (horizontally), the size of the element decreases and thus, the tendency of the nucleus to attract the electrons towards itself increases, meaning the electronegativity increases.

Complete Step by Step Solution:
Valency is the combining capacity of an atom. It is equal to the maximum oxidation state of the atom. Oxygen is a non-metal belonging to group \[VIII\]A. Thus, it has a high tendency to combine with less electronegative elements. The electronegativity is decreasing along the period so oxygen combining tendency also decreases along the period.

Oxygen loses two electrons to achieve the noble gas configuration of neon and mainly exists in the form of oxide having formula ${O^{2 - }}$.
Form groups \[I\]A to \[VII\]A, the number of electrons in the last shell called the valence shell increases with increases thus, the valency of the element also increases one by one from \[I\]A to \[VII\]A.
For example, in sodium oxide the valency of sodium is $1$whereas the valency of magnesium in magnesium oxide is $2$.

Each group has its valency in accordance to achieve the noble gas configuration and then combines with oppositely charged ions to neutralise its charge and form ionic compounds.
Thus, the correct option is A.

Note: Valency is different from the oxidation number. Valency is without positive or negative sign and it is fixed. For s block valency is the same as group number. For p block the valency is group number minus $12$.