Calculate the effective nuclear charge of Na+ ion
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Answered by
58
The reduction produced in the force of attraction due to the presence of intervening electrons is called “shielding effect".
The nuclear charge is decreased by the quantity, “sigma" which is called screening constant.
This decreased nuclear charge is equal to (Z - sigma) is called effective nuclear charge and is denoted by “Zeff”. Or effective nuclear charge (Zeff) is defined as the actual nuclear charge(Z or Z.actual) minus the screening constant(sigma) produced by the electrons residing between the nucleus and the outer-most shell electron(intervening electron).
Zeff = Z - sigma
Sigma is a measure of the extent to which the intervening electrons screen the outer-most shell electron from the nuclear pull on it.
For determining effective nuclear charge on sodium(Na), we apply Slater's rules for calculating sigma and Zeff. These rules are given below:
a) Each of the remaining electrons in the nth shell makes a contribution of 0.35 to the value of sigma.
b) Each of the electrons in(n - 1) th shell makes a contribution of 0.85.
c) Each of the electrons in the next inner shells makes a contribution of 1.0.
d) If sigma is being calculated for an electron of 1s orbital, there will be a contribution of 0.30 from other single electron in 1s orbital. Thus sigma for an electron residing in ns or np orbital = 0.35 x (no. of remaining electrons in nth shell) + 0.85 x (no. of electrons in n - 1th shell) + 1.0 x (no. of electrons in the inner shell)
Now we apply this for sodium(Na),
Na(Z=11) = 1s2(K- shell) 2s2,2p6(L-shell) 3s1(M-shell)
Sigma for 3s1 electron(M-shell electron) = (0.35 x 0) + (0.85 x 8) + (1.0 x 2) = 8.8
Zeff experienced by 3s1 electron = 11 - 8.8= 2.2
The nuclear charge is decreased by the quantity, “sigma" which is called screening constant.
This decreased nuclear charge is equal to (Z - sigma) is called effective nuclear charge and is denoted by “Zeff”. Or effective nuclear charge (Zeff) is defined as the actual nuclear charge(Z or Z.actual) minus the screening constant(sigma) produced by the electrons residing between the nucleus and the outer-most shell electron(intervening electron).
Zeff = Z - sigma
Sigma is a measure of the extent to which the intervening electrons screen the outer-most shell electron from the nuclear pull on it.
For determining effective nuclear charge on sodium(Na), we apply Slater's rules for calculating sigma and Zeff. These rules are given below:
a) Each of the remaining electrons in the nth shell makes a contribution of 0.35 to the value of sigma.
b) Each of the electrons in(n - 1) th shell makes a contribution of 0.85.
c) Each of the electrons in the next inner shells makes a contribution of 1.0.
d) If sigma is being calculated for an electron of 1s orbital, there will be a contribution of 0.30 from other single electron in 1s orbital. Thus sigma for an electron residing in ns or np orbital = 0.35 x (no. of remaining electrons in nth shell) + 0.85 x (no. of electrons in n - 1th shell) + 1.0 x (no. of electrons in the inner shell)
Now we apply this for sodium(Na),
Na(Z=11) = 1s2(K- shell) 2s2,2p6(L-shell) 3s1(M-shell)
Sigma for 3s1 electron(M-shell electron) = (0.35 x 0) + (0.85 x 8) + (1.0 x 2) = 8.8
Zeff experienced by 3s1 electron = 11 - 8.8= 2.2
Answered by
5
Explanation:
screening constant can be represented by sigma.
for s and p block elements screening constant is:
sigma=(number of valence electrons×0.35)+(number of (n-1)×0.85)+(rest of electrons×1)
For sodium(Na):
Na(11)=1s2 2s2 2p6 3s1
hence sodium is a s block element.so
(0×0.35)+(8×0.85)+(2×1)
=8.8
Effective nuclear charge =z-sigma
where z is atomic number
11-8.8=2.2
effective nuclear charge of sodium is 2.2
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