what is the longest wavelength seen in the visible absorption spectrum of Li2+ at ordirnary temperatures?

okay so i was given this equation to apply it to,

okay so i got

delta E=Ro (1/n^2-1/nf^2)

=2.18x10^-18J (1/inifinity- 1/3^2) the three because 3 can be used for longest wavelegnth, and that is n=3

=-7.72x10^19

then ( the symbol that looks like a weird H)=ch/delta E

=3.00x10^8m/s x 6.63x10^-34 / (7.27x10^-19J

=2.735x10^-7m x 10^9nm/1m

=273.5nm

what is the shortest wavelenth using the same equation?

delta E= Ro (1/n^2-1/nf^2)

=2.18x10^-18J (1/inifinity/1/2^2)

=-2.18X 10^-18 x 1/4

=5.45x10^-19J

then(weird H looking symbol)= ch/delta e

=3.00x10^8m/s x 6.63 x 10^-34 Js/(5.45x 10^19J

=3.65x10^-7m x 10^9nm/1m

=365nm

then calculate the ionization energy of Li2+ refer to the exercise 8.55 for the equation needed, to allow for the difference between the nuclear charges of lithium and hydrogn

so....

En = -(2.18x10^-18J) Z^2(1/n^2)

n= principal quantum number

z=atomic number of the element

En= -(2.18x10^-18J)3^2(1/9^2)

but the answer doesnt make sense,

so either my lithium is incorrect,

but the lithium z= 3

and the n = 9 squared which is 81?

??

any help at all would be useful,

i was given these equations to use, so any help would be grateful

thank you

now i know this is wrong because i checked, so if possible is there an alternate

way of calculating this,

the numerbs i got above was from an example i got from my teacher,

which i got told were wrong. so is there another way to go about this???