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Please tell briefly about the effective nuclear charge and rules and how can it be determined.

Please tell briefly about the effective nuclear charge and rules and how can it be determined.

Grade:12

2 Answers

Akash Kumar Dutta
98 Points
8 years ago

Dear Bayana,
efective nuclear charge can be determined by a simple formula
:-
write its electronic configuration in s,p,d,f
then

*electrons at (n) orbit contribute .35 to screening constant except the last electron.
*electrons at (n-1) orbit contribute .8 to screening constant.
*electrons at (n-2) and below contribute to 1 to screenig constant.
then add total value to get the SCREENING CONSTANT=S.
Eg. screening constant for magnesium:-
                         Mg =  1s(2)  2s(2)  2p(6)  3s(2)      
screening constant =  2.1  + (2+6). (.8)  + (2-1)(.35)
                               = 2+6.4+.35
                               = 8.75
HENCE [ENC]= Z(Atomic no.) - (Screening constant)= 12-8.75 = 3.25
Hence we can compare the ENC for any atoms of the element by this simple rule.
It helped me immensly....hope the same with you.
Regards.

pushpendra bansal
19 Points
7 years ago

 

However, in an atom with many electrons the outer electrons are simultaneously attracted to the positive nucleus and repelled by the negatively charged electrons. The effective nuclear charge on such an electron is given by the following equation:

Z_{\mbox{eff}} = Z - S
where z is atomic number

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

  1. An amount of 0.35 from each other electron within the same group
  2.  except for the [1s] group, where the other electron contributes only 0.30.
  3.  an amount of 0.85 from each electron with principal quantum number (n) one less and an amount of 1.00 for each electron with an even smaller principal quantum numbe

Example

iron atom which has nuclear charge 26 and electronic configuration 1s22s22p63s23p63d64s2. The screening constant, and subsequently the effective nuclear charge for each electron is deduced as

 \begin{matrix}   4s     &: 0.35 \times 1& + &0.85 \times 14 &+& 1.00 \times 10 &=& 22.25 &\Rightarrow& Z_{\mathrm{eff}}(4s)=3.75\\   3d     &: 0.35 \times 5&   &               &+& 1.00 \times 18 &=& 19.75 &\Rightarrow& Z_{\mathrm{eff}}(3d)=6.25\\ 3s,3p    &: 0.35 \times 7& + &0.85 \times  8 &+& 1.00 \times  2 &=& 11.25 &\Rightarrow& Z_{\mathrm{eff}}(3s,3p)=14.75\\ 2s,2p    &: 0.35 \times 7& + &0.85 \times  2 & &                &=& 4.15  &\Rightarrow& Z_{\mathrm{eff}}(2s,2p)=21.85\\ 1s       &: 0.30 \times 1&   &               & &                &=& 0.30  &\Rightarrow& Z_{\mathrm{eff}}(1s)=25.7 \end{matrix}

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