Why does atomic radius decrease across a period

Across a period, electrons are added to the same principal energy level while protons are added to the nucleus. The extra protons raise the positive charge felt by the outer electrons, but the inner‑shell electrons cannot completely shield this charge. As a result the electron cloud contracts and the measured atomic radius gets smaller from left to right.

Effective Nuclear Charge (Z_{eff})

Effective nuclear charge is defined as Z_{eff}=Z-S, where Z is the atomic number and S is the shielding constant. For sodium (Z=11) the 10 inner electrons give S≈10, so Z_{eff}\approx1. For chlorine (Z=17) the 10 inner electrons still give S≈10, so Z_{eff}\approx7. The larger Z_{eff} in chlorine pulls its 3p electrons tighter, reducing the radius from about 186 pm (Na) to 99 pm (Cl). This simple calculation illustrates why radius shrinks across the period.

Shielding is most effective when electrons occupy lower‑energy shells; electrons in the same shell shield each other only partially. Because the added electrons across a period stay in the same n‑level, the increase in S is modest, while Z rises sharply. Consequently the net pull on the outer electrons grows, outweighing any slight increase in electron‑electron repulsion, and the atom contracts.

Key factors that influence atomic radius:

• Increasing nuclear charge (more protons)
• Degree of shielding by inner electrons
• Principal quantum number (same across a period)
• Electron‑electron repulsion within the valence shell

Procedure to estimate radius change across a period:

1. 1Write the electron configuration for each element
2. 2Identify the valence shell (same n for the period)
3. 3Calculate Z_{eff}=Z-S using a simple shielding rule
4. 4Observe that Z_{eff} rises while n stays constant, predicting a smaller radius

Typical atomic radii and Z_{eff} values for period 3 elements:

When studying periodic trends, remember that radius depends on the balance between nuclear attraction and electron shielding. Since the principal quantum number does not change across a period, the dominant effect is the rising Z_{eff}, which makes the atom smaller. On exams, compare two elements in the same period and look at their Z values; the one with the higher Z will have the shorter radius.