Calculating effective nuclear charge

[escryan]

Homework Statement

If ionization energy is 899.4 kJ/mol for Be, what is the effective nuclear charge?

Homework Equations

Z_eff = Z - S

E=R_H(Z²/n²) ??
E=R_H(Z_eff²/n²)??

The Attempt at a Solution

My attempted solution was subbing into
Z_eff = Z - S
Z_eff = 4 - 2
= 2

But I suspect that is wrong... because why ionization energy is given.. so shouldn't it be used in the calculation?

And somewhere I think I read that "S" was supposed to be a "constant" of some sort, and I just subbed 2 in because I thought that it was the number of electrons in the first orbital ?

 

[Borek]

One of the equations you listed contains both ionization energy and effective nuclear charge, why don't you use it?

 

[escryan]

Ah..
So subbing in values
E=899.4 kJ/mol
R_H=2.178 x 10^-21 kJ
n=1

I get Z²_eff= 4.129 x 10 ²³ mol

How does one get to the units/value of Z²_eff after this?

 

[Borek]

Ionization energy was per mole, not per molecule.

 

[escryan]

Oops, just noticed that "Z²_eff= 4.129 x 10 23 mol " should actually read "Z²_eff= 4.129 x 10 23 mol^-1 "

I think that the italicized part is what confuses me the most -- what are the units for this portion? I'm going to take a guess that it is currently molecules/mol, but if so, is this always the case whenever expressing a value and the unit mol^-1?

Like for this example, what was given was in kJ/mol. When the kJs were cancelled, what resulted was just mol^-1...