Calcualte the effective nuclear charge ( Z^*) of Na⁺.

p.s. Don't know to which class this question would belong to!:P I'm reading it in IIT coaching!

Dear student!

We have, effective nuclear charge,

 Z* = Z - σ,  Where, Z= Atomic number, σ = Shielding or screening constant.

To calculate screening constant, we need to write e.c of sodium (Na)= 1s² 2s² 2p⁶ 3s¹,  

For, sodium ion Na⁺ =  1s² 2s² 2p⁶  

The shielding constant is calculated as:

The shielding constant for each group is formed as the sum of the following contributions:

All other electrons in the same group as the electron of interest shield to an extent of 0.35 nuclear charge units except 1s group, where the other electron contributes only 0.30.

If the group is of the [s, p] type, an amount of 0.85 from each electron (n-1) shell and an amount of 1.00 for each electron from (n-2) and lower shell.

If the group is of the [d] or [f] type then an amount of 1.00 for each electron from all lying left to that orbital.

So, nth level(3s 3p) contributes zero electrons, (n-1) level has 6 and (n-2) level has 2 electrons so,

σ =  0.85 x 8 + 1 x2 = 6.8 +2 = 8.8 

So,  Z* = Z - σ = 11-8 .8 =  2.2