Effective nuclear charge and Ionization energy

Question

A common reason given on why 3rd ionization energy > 2nd > 1st is because of increasing effective nuclear charge.

As per my book $Z_\mathrm{eff}$ = Atomic number $-$ Number of inner electrons.

Now let us consider a Carbon atom. C has an Electronic configuration of $\ce{[He] 2s^2 2p^2}$ or $2,4$

Right now the effective nuclear charge is $6 - 2 = 4$

Now if we remove the first electron the first ionization energy will be $=\pu{1086.45 kJ/mol}$

After doing this effective nuclear chrarge is still $6 - 2 = 4$

Now if we remove the second electron the second ionization energy will be $=\pu{2352.62 kJ/mol}$

If the effective nuclear charge in removal of 1st and 2nd electron is same then why is 2nd ionization energy > 1st.

note : these values are taken from here

Answer 1

Effective nuclear charge $Z_{\text{eff}}$ is given by Slater's Rules.

According to these rules, for $\ce{C}$, effective nuclear charge experienced by an outer shell electron is: $$Z_{\text{eff}} = 6 - 0.85\times 2 - 0.35\times 3 = 3.25$$

For $\ce{C+}$, effective nuclear charge is $$Z_{\text{eff}} = 6 - 0.85\times 2 - 0.35\times 2=3.6$$

Since the effective charge for $\ce{C+}$ is more than that on $\ce{C}$, the second ionisation energy is more than that of the first.