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How does the number of (i) valence electrons (ii) valency; vary on moving from left to right: (a) In the second period of a periodic table? (b) In the third period of a periodic table?

Answer
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Hint: The valence electrons are the last shell electrons .the number of valence shell electrons goes on increasing across the period. The valency determines the reactivity of the element. The trend for valency is first increasing from group 1 till group 14 and then decreases down to zero from the 15-18 group.

Complete answer:
1) Valence electrons:
The electrons in the outer energy levels of an atom are called the valence electrons. Valence electrons participate in the interaction with the atoms. This is the electrons that are located far away from the nucleus and thus due to the shielding effect less attracted by the nucleus. However, these electrons have an affinity towards the nucleus of another atom.
The total number of valence electrons in an atom is depicted by the position of an atom in the periodic table. Across the period the valence electrons or number of electrons in the last shell increases from group 1-2 and then from 13 to 18.
-In the second period, the last shell electrons enter into the $\text{n=2}$ shell. Thus the valence electrons increase from lithium to the neon. Such that the valence electron for lithium is 1 and as we move across the period the valence electron for the group 18 element which is for neon is 8.
A similar trend is observed in the third period. The last shell electron enters in the third shell. The valence electrons increase from sodium to argon.
All the elements in the same group have the same number of valence electrons thus have similar chemical properties.
2) Valency:
The valency or valence is the measure of the combining power of an element with other elements to form a compound or molecule.in other words, this is the total number of electrons donated or gained by the element to attain the nearest noble gas configuration.
In the second period, the last shell electrons are in the second orbital. The valency for the period is found to be one for alkali metal. It increases till it reaches group 14 which has valency as the 4.Fromgroup 15 the valency again starts to decrease and finally becomes zero for neon. This is because lithium can donate an electron to attain the helium configuration. However for group 15, the last shell holds 8 electrons and it required the 3 more electrons to attain the neon configuration.
A similar trend of valency is observed in the third period.

Note:
The total number of valence electrons in the shell decides its reactivity, whether it is highly reactive or unreactive. For reactive atoms, the number of valence electrons also decide whether they gain or lose the electron. The group 14 elements have valency 4.They can either accept or donate their four electrons to attain Noble gas configuration. However, it takes high ionization enthalpy. Thus they form a bond by sharing its electrons with atoms.