An element \(A\) is tetravalent and another element \(B\) is divalent. The formula of the compound formed from these elements will be : (a) \(A_{2} B\) (b) \(A B\) (c) \(A B_{2}\) (d) \(A_{2} B_{3}\)

Understanding valency is crucial when it comes to the formation of compounds. Valency represents the ability of an atom to bond with other atoms, indicating the number of electron pairs an atom is willing to share, gain, or lose to acquire a full outer shell, following the octet rule. For example, if an element is tetravalent (like carbon or silicon), it means it has 4 electrons available for sharing with other atoms.

When elements with different valencies (say a tetravalent and a divalent element) come together, they do so in a way that satisfies both elements' need to achieve stability. The resulting compound is electrically neutral because the total number of electrons lost by one element is equal to the number of electrons gained by the other. If any part of this idea seems perplexing, remember that the ultimate goal is stability; everything that atoms 'do' in chemical reactions is to attain a more stable, lower-energy state.

The criss-cross method is a shortcut to determine the correct formula for a compound formed between two elements. This technique involves taking the valency numbers of the two elements and 'criss-crossing' them, meaning the valency of one becomes the subscript of the other element in the chemical formula. It's important to ensure that the formula is expressed in the lowest whole number ratio.

For instance, if element A is tetravalent and element B is divalent, we write the symbols and their valencies as A(4) and B(2). By criss-crossing, we place the 4 as the subscript for B and the 2 as the subscript for A, getting initially A₂B₄. Don't forget, however, that this is not the final step! Subscripts in a chemical formula should be the smallest possible whole numbers that maintain the ratio indicated by the valencies, hence this formula would be reduced to AB₂, a much simpler form.

Elements can have different valencies, and understanding these is key for predicting compound formation. Tetravalent elements, with a valency of four, are capable of forming four bonds with other elements. Carbon, for example, is a classic tetravalent element, forming the backbone of all organic chemistry. Its ability to bond with up to four other atoms makes it incredibly versatile and is the reason for the diversity of organic compounds.

On the other hand, divalent elements like calcium or magnesium have a valency of two, which means they can form two bonds. In a compound, a divalent element typically pairs with another divalent element, or two monovalent elements, to achieve stability. This pairing, however, must conform to the rules of chemical bonding, which strive to balance out the positive and negative charges to result in a neutral compound.