Effective Nuclear Charge for Sodium Atom

[James Brady]

Homework Statement

The 3s state Na has an energy of -5.14 eV. Determine the effective nuclear charge.

Homework Equations

$Z_{eff} = Z - s$ Where Z is the atomic number and s is the number of shells in inner orbits.

The Attempt at a Solution

The textbook doesn't go into much more detail than this. All I have is $Z_{eff} = 11 - 10 = 1e$ The correct answer is 1.14e. How do I incorporate energy into my calculations. I understand that that a higher negative energy would imply a higher effective charge because of the greater attraction, but analytically, I do not know how to get there.

 

[drvrm]

The textbook doesn't go into much more detail than this. All I have is Zeff=11−10=1eZeff=11−10=1eZ_{eff} = 11 - 10 = 1e The correct answer is 1.14e.

there are some ways to calculate it-
http://www.wikihow.com/Determine-Screening-Constant-and-Effective-Nuclear-Charge

How do I incorporate energy into my calculations.

write down the equation for energy state and use it to calculate zeffective