Effective Nuclear Charge Calculator

An effective nuclear charge calculator is a tool used in chemistry to determine the net positive charge experienced by an electron in a multi-electron atom.

Consider a sodium atom with 11 protons in its nucleus. The outermost electron doesn’t experience the full +11 charge due to the shielding effect of the inner electrons.

If we input the atomic number (11) and the number of inner electrons (10) into the calculator, it determine that the effective nuclear charge for the outermost electron in sodium is approximately +2.51. This means the valence electron experiences a charge equivalent to about 2.51 protons rather than the full 11 protons in the nucleus.

Effective Nuclear Charge Periodic Chart

Effective Nuclear Charge Formula

The formula for calculating the Effective Nuclear Charge (Z_eff) is:

Z_eff = Z - S

Where:

• Z is the atomic number (number of protons in the nucleus)
• S is the shielding constant (the effect of electron shielding)

Inner Shell Electrons (n-1):

S = 0.85 per electron

S(inner) = 0.85 × number of inner electrons

Same Shell Electrons (n):

S = 0.35 per electron

S(same) = 0.35 × number of same-shell electrons

Outer Shell Electrons (n+1):

S = 0 (no shielding effect)

Practical Example: For Sodium (Na, Z=11):

Zeff = 11 - (10 × 0.85)
Zeff = 11 - 8.5 = 2.5

Shielding Rules by Shell:

Consider a chlorine atom (atomic number 17) with 7 valence electrons.

Z = 17 (atomic number of chlorine)

S ≈ 10 (approximate shielding constant for chlorine’s valence electrons)

Z_eff = 17 - 10 = 7

The effective nuclear charge experienced by the valence electrons in chlorine is approximately +7. This means that despite having 17 protons in its nucleus, the outermost electrons of chlorine experience a net charge equivalent to about 7 protons due to the shielding effect of the inner electrons.

What is effective nuclear charge?

Effective nuclear charge refers to the net positive charge experienced by an electron in a multi-electron atom. It’s a crucial concept in understanding atomic properties and chemical behavior. The effective nuclear charge is always less than the actual nuclear charge due to the shielding effect of inner electrons.

For instance a magnesium atom with 12 protons in its nucleus. The two valence electrons in the 3s orbital don’t experience the full +12 charge because the inner electrons (1s, 2s, and 2p) shield them from the nuclear charge. The effective nuclear charge for these valence electrons might be around +3.31, significantly less than the total nuclear charge of +12.