Quantum Numbers

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Effective nuclear charge (Z_eff) experienced by valence electrons increases across a period mainly because:

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1. **Definition**: $Z_{eff} = Z - \sigma$, where $Z$ is the actual nuclear charge (number of protons) and $\sigma$ is the shielding constant.
2. **Trend across Period**: As we move from left to right, one proton is added to the nucleus for each consecutive element.
3. **Shielding Factor**: Electrons are added to the same main valence shell. These electrons do not shield each other very effectively compared to inner-core electrons.
4. **Outcome**: The increase in $Z$ far outweighs the slight increase in shielding from same-shell electrons.
5. **Result**: Valence electrons feel a stronger pull towards the nucleus, leading to a higher **$Z_{eff}$** and a decrease in atomic radius.

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