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Q3.10:
How do atomic radius vary in a period and in a group? How do you explain the variation?

Solution :

1. Variation of Atomic Radius in a Period

As we move from left to right across a period in the periodic table, the atomic radius decreases.

2. Justification for Periodicity

  • Effective Nuclear Charge ($Z_{eff}$): As we traverse a period, the atomic number increases by one unit per element, meaning one proton is added to the nucleus and one electron is added to the same valence shell. [Per Aufbau Principle and shielding effect rules].
  • Incomplete Shielding: Electrons added to the same principal energy level provide poor shielding against the increasing positive charge of the nucleus.
  • Resultant Contraction: Consequently, the $Z_{eff}$ experienced by the valence electrons increases. This higher electrostatic attraction pulls the electron cloud closer to the nucleus, causing the atomic radius to shrink.

3. Variation of Atomic Radius in a Group

As we move down a group in the periodic table, the atomic radius increases.

4. Justification for Group Variation

  • Increase in Principal Quantum Number ($n$): Moving down a group, each successive element adds an entirely new electron shell (principal energy level). [Per Bohr's Model of the Atom].
  • Screening Effect: The inner shells of electrons act as a screen, shielding the valence electrons from the full attractive force of the nucleus. This phenomenon is known as the Screening Effect or Shielding Effect.
  • Dominance of Distance: Although the nuclear charge increases down the group, the increase in the number of shells and the resulting increase in distance between the nucleus and the valence electrons ($r \propto n^2$) significantly outweighs the increase in nuclear attraction.

5. Visual Representation of Trends

Trend across a Period (Left to Right) Trend down a Group Increase

6. Comparative Data Analysis

Direction Atomic Radius Trend Primary Factor
Across Period Decreases Increasing $Z_{eff}$
Down Group Increases Increasing Number of Shells ($n$)

Final Solution: The atomic radius decreases along a period due to an increase in effective nuclear charge ($Z_{eff}$) pulling electrons closer to the nucleus, while it increases down a group due to the addition of new principal energy shells that offset the increased nuclear attraction.


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