# How do you calculate the second ionization energy of Helium?

##### 1 Answer

You can do it by calculating the first ionization energy of

#"He"(g) -> "He"^(+)(g) + e^(-)# ,#" "" "DeltaH_(IE_1)#

#"He"^(+)(g) -> "He"^(2+)(g) + e^(-)# ,#" "DeltaH_(IE_2)#

As **Koopman's approximation theorem**, which in simplified terms, states...

For a one-electron orbital, the potential energy of that orbital is opposite in sign to the ionization energy from that orbital.

Thus, we just need to get the magnitude of

#E_n = -Z^2cdot"13.61 eV"/n^2# where

#Z# is the atomic number and#n# is the principal quantum number. And naturally,#-"13.61 eV"# is the ground-state energy of hydrogen atom.

#color(blue)(DeltaH_(IE_2)) = |E_1("He"^(+))| = |-2^2cdot"13.61 eV"/1^2|#

#=# #ulcolor(blue)("54.44 eV")#