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Why do all the elements of the (a) same group have similar properties, (b) same period have different properties?

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Why do all the elements of the

(a) same group have similar properties,

(b) same period have different properties?

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(a) Elements of same group have similar properties due to same number of valence electrons, therefore, they have same valency.

(b) Elements of same period have different properties as they differ in number of valence electrons.

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