Why does this equation not give me the ionization energy of lithium?

[patric44]

Homework Statement

i want to find the first ionization energy for lithium using Bohr formula but something seems wrong !

Relevant Equations

Bohr energy equation

i am trying to calculate the first ionization energy for lithium with this equation but it seems to work only with hydrogen ?
i put nf = infinity and ni =2 ,and z = 3 for lithium and it gives about 30 ev not 5.39172 ev which is the value for lithium :

i will appreciate any help in this

 

[Borek]

There are some limitations to the Bohr model, do you know them?

 

[patric44]

There are some limitations to the Bohr model, do you know them?

i know that it failed to describe the experimental results for multi electron atoms ,
so what equation is being used for finding the ionization energy ?
because every where i look online it seems that people uses that equation ?!

 

[mjc123]

Look up "Rydberg atom". Your equation is for a hydrogen-like ion, with 1 electron, i.e. Li²⁺.

 

[patric44]

Look up "Rydberg atom". Your equation is for a hydrogen-like ion, with 1 electron, i.e. Li²⁺.

thanks i got it now , so i am assuming that there is no equation that could calculate the first ionization energy of a specific element except hydrogen ?!
or even approximately at least ?

 

[mjc123]

Not really, without computer number-crunching. Practically, I think it would work the other way round - measure the ionisation energy, calculate the quantum defect, compare periodic trends and see what that tells you about the orbitals.