Define IE₁ and IE₂. Why IE₂ > IE₁ for a given atom? Discuss the factors that effect IE of an element.

IE₁: The amount of energy required to remove an electron from outermost orbital of isolated neutral gaseous atom is called IE₁.
${\mathrm{X}}_{\left(\mathrm{g}\right)}+{\mathrm{IE}}_1\to {\mathrm{X}}_{\left(\mathrm{g}\right)}^{+}+{\mathrm{e}}^{\ominus }$
IE₂ : The amount of energy required to remove an electron from unipositive gaseous ion is called IE₂.
${\mathrm{X}}_{\left(\mathrm{g}\right)}^{+}+{\mathrm{IE}}_2\to {\mathrm{X}}_{\left(\mathrm{g}\right)}^{2+}+{\mathrm{e}}^{\ominus }$
I.E₂ > I.E₁ because in unipositive ion number of protons are more than the number of electrons, so the nuclear attraction increases on electrons.
Factors effecting on I.E :
1) Atomic size :
As atomic size increases, I.E value decreases.
As atomic size decreases, I.E value increases.
$\text{ I.E }\alpha \frac{1}{\text{ Atomic size }}$
2) Nuclear charge :
As nuclear charge increases, I.E value is also increases. If nuclear charge value decreases,
I.E value decrease.
I.E $\propto$ Nuclear charge
3) Screening effect :
If Screening effect increases, IE value decreases. If screening effect decreases, I.E value increases.
$\text{ I.E }\mathrm{\alpha }\frac{1}{\text{ Screening effect }}$
4) Electronic configuration :
Half filled (or) full filled orbitals of an atom are more stable. So they have more I.E. value.