The relationship between atomic number (Z) , effective nuclear charge ( Z_eff) and shielding constant (σ) is: 

CONCEPT:

Effective Nuclear Charge (Z_eff)

• Effective nuclear charge (Z_eff) is the net positive charge experienced by an electron in a multi-electron atom.
• Z_eff accounts for the shielding or screening effect of inner electrons that reduce the full attractive force of the nucleus on the outer electrons.
• The shielding constant (σ) quantifies the extent to which inner electrons block the nuclear charge from outer electrons.
• The relationship between the atomic number (Z), effective nuclear charge (Z_eff), and shielding constant (σ) is given by the formula:

  Z_eff = Z - σ

EXPLANATION:

• The atomic number (Z) represents the total number of protons in the nucleus of an atom.
• The shielding constant (σ) represents the reduction in nuclear attraction due to the repulsion caused by inner electrons.
• The effective nuclear charge (Z_eff) is the actual positive charge "felt" by an electron after accounting for the shielding effect.
• Using the relationship Z_eff = Z - σ:
  • If Z is the total nuclear charge and σ is the shielding constant, subtracting σ from Z gives the net effective nuclear charge (Z_eff).
• Z_eff = Z - σ (Correct, as it accurately represents the relationship).

​Therefore, the correct answer is Z_eff = Z - σ.