Register to reply

Calculating Effective Nuclear Charge using Ionization Energy

by doublavay
Tags: charge, electron, energy, ionization, nuclear
Share this thread:
doublavay
#1
Nov24-09, 05:58 PM
P: 2
Find the effective nuclear charge of the outermost electron in sodium using its ionization energy.

Ionization energy of sodium = 5.14 eV = 8.23e-19 J
Zeff = Z - S

I tried using the equation Zeff = Z - S, but when I followed all the rules, I found

S = (8*0.85)+(2*1.00) = 8.8
Zeff = 11 - 8.8 = 2.2

but the answer in my book says that it should be 1.8, and that method didn't use the ionization energy of sodium. I need to find an equation that explains quantitatively how ionization energy relates to Zeff.
Phys.Org News Partner Science news on Phys.org
New model helps explain how provisions promote or reduce wildlife disease
Stress can make hard-working mongooses less likely to help in the future
Grammatical habits in written English reveal linguistic features of non-native speakers' languages
Redbelly98
#2
Nov27-09, 05:23 PM
Mentor
Redbelly98's Avatar
P: 12,064
Welcome to Physics Forums! And sorry for the delay in responding.

Up until the last 10 minutes, I was not familiar with this type of problem. After a google search, I am now familiar with two ways to solve this problem.

One way is the way you did it, but they don't seem to want that. The other way is shown here, look at the equation for Zeff:

http://www.physicsforums.com/showthread.php?t=266326

That way does make use of the ionization potential. You'll have to use the appropriate value of n as well, of course.
doublavay
#3
Nov28-09, 09:34 PM
P: 2
I'm still having trouble with this problem, because E = RH (Zeff / n)2 doesn't seem to have units that cancel out. Energy is measured in Joules or eV, but RH is the only thing with units on the other side of the equation, and it has units of m-1. Or maybe I'm using the wrong value of RH... I thought it was just the Rydberg constant multiplied by 1(because it's Hydrogen). Is that incorrect?

Redbelly98
#4
Nov29-09, 06:48 AM
Mentor
Redbelly98's Avatar
P: 12,064
Calculating Effective Nuclear Charge using Ionization Energy

It's good to know that some people still pay attention to units

RH, with the units of m-1, is 1/λ for ionization of the hydrogen atom. Instead, use the Rydberg constant in eV, which may be found in the Atomic constants section here:

http://www.pnc.aps.anl.gov/info/Phys...ants_1986.html

(This is simply the ionization energy of Hydrogen.)


Register to reply

Related Discussions
Calculating First Ionization Energy Biology, Chemistry & Other Homework 2
Atomic structure and determing effective nuclear charge Advanced Physics Homework 4
Calculating effective nuclear charge Biology, Chemistry & Other Homework 4
Calculating the Kinetic Energy of a Point Charge From Far Away Introductory Physics Homework 0
Ionization and nuclear fission in the foggoid General Physics 0