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How would you explain why the trend of electron affinity is increasing from left to right and decreasing from up to down?

Answer
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Hint:The trends in the periodic table can be observed on the basis of their size differences while moving from across a period or down the group.
As we move across a period, the size of the atom decreases as the nuclear charge increases but only one electron is added with increase of each period. While in case of moving down the group, the size increases as an outermost shell is added with increase of each group.

Complete step-by-step answer: In order to answer this question we must first understand the term electron affinity. It is the energy required by an isolated gaseous atom to add an electron to its outermost shell. In other words the electron affinity of an atom is the change in energy observed in that atom when an electron is added to it, and the charge on the neutral atom becomes negative.
Now, when we move from left to right across a period the electron affinity of the atom increases gradually. This is because of the decrease in size of the atom on moving from left to right, as an electron is added on every consequent element, and the nuclear charge increases on the same.
When we move from up to down in a group, the gradual decrease of electron affinity can be observed. This is because the size of the atom increases on moving down the group, as with each group, a new outermost orbital is added and the effective nuclear charge experienced by the outermost electrons decreases.

Note:
The energy required by an isolated gaseous atom to add an electron to its outermost shell, is termed as the electron affinity.
It increases on moving across a period as the size of the atom decreases gradually. Whereas, it decreases on moving down the group, because of the gradual increase in size.