Calculating effective nuclear charge

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Discussion Overview

The discussion revolves around calculating the effective nuclear charge (Zeff) for beryllium (Be) using its ionization energy. Participants explore the relationship between ionization energy, effective nuclear charge, and the relevant equations, while addressing units and assumptions involved in the calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant attempts to calculate Zeff using the formula Zeff = Z - S, substituting Z=4 and S=2, arriving at Zeff=2, but expresses doubt about this approach given the ionization energy provided.
  • Another participant suggests using the equation that incorporates both ionization energy and effective nuclear charge, prompting a reevaluation of the initial calculation.
  • A participant calculates Z2eff using the provided ionization energy and other constants, but questions how to derive the units and value of Z2eff from their calculation.
  • Clarification is made that ionization energy is given per mole, not per molecule, which may affect the calculations.
  • A participant corrects their earlier statement regarding the units of Z2eff, expressing confusion about the implications of the unit mol-1 in their context and its relation to other values expressed in kJ/mol.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct approach to calculating effective nuclear charge or the interpretation of units involved in the calculations. Multiple viewpoints and uncertainties remain regarding the application of ionization energy in the context of Zeff.

Contextual Notes

Participants note potential limitations in their understanding of the constants used in the calculations and the implications of units, indicating that assumptions about the values of S and the interpretation of ionization energy may not be fully resolved.

escryan
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Homework Statement



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

Homework Equations


Zeff = Z - S

E=RH(Z2/n2) ??
E=RH(Zeff2/n2)??

The Attempt at a Solution



My attempted solution was subbing into
Zeff = Z - S
Zeff = 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 ?
 
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One of the equations you listed contains both ionization energy and effective nuclear charge, why don't you use it?
 
Ah..
So subbing in values
E=899.4 kJ/mol
RH=2.178 x 10-21 kJ
n=1

I get Z2eff= 4.129 x 10 23 mol

How does one get to the units/value of Z2eff after this?
 
Ionization energy was per mole, not per molecule.
 
Oops, just noticed that "Z2eff= 4.129 x 10 23 mol " should actually read "Z2eff= 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...
 

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