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Dear Student,
The energy released when an electron is added to a neutral gaseous isolated atom to form a negatively charged ion is called Electron Affinity.
one word phrase is Electron Affinity

i) Inert gases have already achieved octet that means their outermost shells are filled with electrons always so they do not tend to react with any element thereby as they do not react so they do not form ions. The electronic configuration of inert gases is ns2np6. Therefore they have completely filled orbitals that imparts high stability to the gases and thus they don't ionises. 

ii) Moving left to right within a period, As the atomic radius decreases, it becomes harder to remove an electron that is closer to a more positively charged nucleus hence the ionisation energy increase from left to right. 
I) Higher  because of the increasing strength of the metallic bonds. (that is the element B would have higher metallic character than A)
II) higher as electro affinity increases from left to right. (that is the element A would probably have higher electron affinity than B)
III) smaller due to more number of nucleons. As nucleons increases the effective force on outer most shell electrons also increases hence the radius decreases. (that is the element A would have smaller atomic size than B.)


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