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Assertion: Electronegativity across a period increases and down the group decreases
Reason: As we move down the group basic character increases while as we move across a period acidic character increases
A. Both assertion and reason are correct and reason is the correct explanation for assertion.
B. Both assertion and reason are correct and reason is not the correct explanation for assertion.
C. Assertion is correct but reason is incorrect
D. Both assertion and reason are incorrect

Answer
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Hint: As we move down the group size of the atom increases and as we move across a period size of the atom decreases. Now size is a very important thing related to an atom as small size means periphery of the atom is nearer to the nucleus and effect of nuclear charge will be more prominent while bigger size means it is distant from nucleus and effect of nuclear charge will be less prominent.

Complete step by step answer:
As size of the atom decreases across the period, therefore effective nuclear force increases across the period, it means any electron that will come near to the nucleus will feel the more attraction towards it, that suggests that across the period electronegativity will increase.
As size of the atom increases down the group, therefore effective nuclear force decreases across the group, it means any electron that will come near to the nucleus will feel the less attraction towards it, that suggests that down the group electronegativity will decrease.
So the assertion is correct.
As we move across the period, electronegativity increases, that means tendency to gain electron increases, non-metallic character increases, acidic strength of their compounds with hydrogen increases, acidic strength of their oxides increases.
As we move down the group, electronegativity decreases, that means tendency to lose electron increases, metallic character increases, basic strength of their compounds with hydrogen increases, basic strength of their oxides increases.
So the reason is also correct.
But we can see that the reason is not explaining the assertion.

Correct answer for this question is Option (B).

Additional information:
Oxides of non-metals give hydrogen ions in water that’s why oxides of the elements like sulfur and nitrogen are major contributors to the acid rain as their oxides form when fuel burns and these gases stay in the atmosphere. During rainfall they dissolve into the water and come down in the form of acid rain.

Note: As atomic size decreases across the period that’s why fluorine has the smallest atom size and the highest electronegativity in the periodic table and also it is the best non-metal. With the exception of noble gases, the elements that are at the right most side on top of the periodic table are the most electronegative elements like oxygen, nitrogen, chlorine etc.