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Dear Student,
 The Decrease in atomic radius across the period not only depends upon the attraction between the nucleus and electrons. Rather it depends on the effective nuclear charge . It is the nuclear attraction acting on each electron. If the atomic number is say for example 5 that means there are 5 e-s and 5e+​ this means that each electron will be attracted by 5 protons. But if the atomic number is 6,now there are 6 e- s and 6ethis means each electron is pulled by 6 protons thereby leading to a decrease in atomic size.
I hope this clears the confusion!
Regards!

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