The energy of an atomic orbital depends on the effective nuclear charge (Z_eff) experienced by the electron. For multi-electron atoms, orbital energy is lower when Z_eff is higher. The 2s orbital energy is lowest in the atom where the 2s electron experiences the highest effective nuclear charge.

Let's analyze each option:

H (Hydrogen): Only one electron, no shielding. Z_eff = 1.

Li (Lithium): Atomic number 3. Electron configuration: 1s²2s¹. The 2s electron is shielded by the 1s² core. Z_eff ≈ 1.28.

Na (Sodium): Atomic number 11. Electron configuration: 1s²2s²2p⁶3s¹. The 2s orbital is now an inner orbital. It experiences a higher Z_eff because it is closer to the nucleus and less shielded than the 3s electron. For a 2s electron in Na, Z_eff is much higher.

K (Potassium): Atomic number 19. Electron configuration: 1s²2s²2p⁶3s²3p⁶4s¹. The 2s orbital is even deeper inside the atom. It experiences the highest effective nuclear charge due to its proximity to the nucleus and poor shielding from other electrons.

The order of increasing effective nuclear charge for a 2s electron is: H < Li < Na < K.

Since lower orbital energy corresponds to higher Z_eff, the energy of the 2s orbital is lowest in K (Potassium).

Related Concepts

Effective Nuclear Charge (Z_eff): The net positive charge experienced by an electron in a multi-electron atom. It is calculated as Z_eff = Z - σ, where Z is the atomic number and σ is the shielding constant. Electrons in inner orbitals experience a higher Z_eff and are more tightly bound (lower energy).

Shielding Effect: The reduction in the effective nuclear charge on an electron due to repulsion by other electrons. Inner electrons shield outer electrons more effectively than electrons in the same shell.

Key Formula

The energy of an orbital is approximately given by: $E=-\frac{13.6Z_{\text{eff}}^2}{n^2}\text{eV}$

This shows that energy becomes more negative (lower) as Z_eff increases.