How to calculate effective nuclear charge and shielding constant for d and f block elements
Please explain with example
How to calculate effective nuclear charge and shielding constant for d and f block elements
Please explain with example
The effective nuclear charge (Zeff or Z*) is the net positive charge experienced by an electron in a polyelectronic atom. The term "effective" is used because the shielding effect of negatively charged electrons prevents higher orbital electrons from experiencing the full nuclear charge of the nucleus due to the repelling effect of inner-layer electrons.
Effective Nuclear Charge Formula
the formula for calculating the effective nuclear charge of a single electron is as follows:
Zeff = Z – S
Here
Zeff = the effective nuclear charge
Z = denotes the number of protons existing in the nucleus
S = average amount of density between the nucleus and the electron.
Screening factor or Screening effect constant-
When we consider the attraction of the nucleus over an electron, there are always some electrons in between these two. These electrons partially neutralise the effect of attraction and thus the effective nuclear charge for an electron is much less than the actual nuclear charge. This screening of inner electrons produces the screening factor. It is represented by ‘σ’. It is related to effective nuclear charge by the following relation-
Effective nuclear charge = Actual nuclear charge – σ
Zeff = Z – σ
Rules to calculate Screening effect-
The most accepted method for the calculation or determination of the value of the screening factor is given by Slater. There are some rules to find screening factor. According to Slater,
1) Each electron of the orbit higher than the electron under consideration contributes zero.
2) Each electron of the same orbit contributes 0.35 except the ‘1s ‘ electron which contributes 0.30.
3) Electron of (n-1) orbit contributes 0.85.
4) All the electrons in the (n-2 ) shell contribute 1.0.
For Example:
30 Zn – 1s2 , 2s2 , 2p6 , 3s2 , 3p6 , 4s2 , 3d10
Screening factor ‘σ ‘ = 1 x 0.35 + 18 x 0.85 + 10 x 1 ‘
σ = 0.35 + 15.30 + 10 = 25.65 Ans.
Zeff = Z – σ
Z = 30
Z eff = 30.0 – 25.65 = 4.35
The effective nuclear charge (Zeff or Z*) is the net positive charge experienced by an electron in a polyelectronic atom. The term "effective" is used because the shielding effect of negatively charged electrons prevents higher orbital electrons from experiencing the full nuclear charge of the nucleus due to the repelling effect of inner-layer electrons.
Effective Nuclear Charge Formula
the formula for calculating the effective nuclear charge of a single electron is as follows:
Zeff = Z – S
Here
Zeff = the effective nuclear charge
Z = denotes the number of protons existing in the nucleus
S = average amount of density between the nucleus and the electron.
Screening factor or Screening effect constant-
When we consider the attraction of the nucleus over an electron, there are always some electrons in between these two. These electrons partially neutralise the effect of attraction and thus the effective nuclear charge for an electron is much less than the actual nuclear charge. This screening of inner electrons produces the screening factor. It is represented by ‘σ’. It is related to effective nuclear charge by the following relation-
Effective nuclear charge = Actual nuclear charge – σ
Zeff = Z – σ
Rules to calculate Screening effect-
The most accepted method for the calculation or determination of the value of the screening factor is given by Slater. There are some rules to find screening factor. According to Slater,
1) Each electron of the orbit higher than the electron under consideration contributes zero.
2) Each electron of the same orbit contributes 0.35 except the ‘1s ‘ electron which contributes 0.30.
3) Electron of (n-1) orbit contributes 0.85.
4) All the electrons in the (n-2 ) shell contribute 1.0.
For Example:
30 Zn – 1s2 , 2s2 , 2p6 , 3s2 , 3p6 , 4s2 , 3d10
Screening factor ‘σ ‘ = 1 x 0.35 + 18 x 0.85 + 10 x 1 ‘
σ = 0.35 + 15.30 + 10 = 25.65 Ans.
Zeff = Z – σ
Z = 30
Z eff = 30.0 – 25.65 = 4.35
