Question

Among elements 1–18, which element or elements have the smallest effective nuclear charge if we use the equation zeff=z−s to calculate zeff? check all that apply.

Answer 1

Slater’s Rules can be used for calculating the effective nuclear charge (Z eff)
The effective nuclear charge is given by the formula
Zeff = Z - S
Where Z is the actual nuclear charge and S is the shielding constant
The value of shielding constant can be determined using the following rules
Rule 1
Write the electronic configuration in the following order
(1s) (2s, 2p) (3s, 3p) (3d) (4s, 4p) (4d) (4f) (5s, 5p)…..
Rule 2. Identify the group of the electron whose effective nuclear charge is to be determined. Ignore all the electrons to the right side of this group
Rule 3. if the electron under consideration is an ‘s’ or ‘p’ orbital, then all other electrons in the same group (ns, np) contributes 0.35 to the shielding constant(S), and all the electrons in the (n- 1) shell contribute 0.85 to the shielding constant. All the other electrons to the left of (n-1) shell contributes a value of 1.00 to the shielding constant.
Rule 4. If the electron under consideration is in ‘d’ or ‘f’ orbital, each additional electrons in the same group contributes 0.35 to shielding constant. All the other electrons to the left contributes 1.00 to shielding constant.
If we use this rule to calculate Zeff of Hydrogen,
H =(1S¹)
Z=1
S=0
Zeff = Z - S = 1-0 =1, which is the smallest Zeff possible.
Smallest Zeff is shown by Hydrogen

Answer 2

Element H have the smallest effective nuclear charge

Further explanation

The effective nuclear charge is the nuclear charge which is influenced by the shielding effect of electrons

The effective nuclear charge (Zeff) can be formulated as:

$\large{\boxed{\bold{Z_{eff}=Z-S}}}$

with

Z = nuclear charge = atomic number

S = shield constant

Shielding constants are constants that are generated from the core attraction of electrons in the inner shell

Rules for calculating shield constants-S (Slater's Rules)

• 1. Electrons in orbitals are grouped according to the shell

/ 1s / 2s, 2p / 3s, 3p / 3d / 4s, 4p / 4d / 4f / 5s, 5p / 5d / 5f /

• 2. The electron to the right of the specified electron, shield constants = 0

• 3. The electron to the left of the specified electron, (for the ns, np orbitals), the value of the shield constant:

* Electrons in the same shell shielding effects (same ns and np orbitals): 0.35

* Electrons in the deeper shell (n-1, in the lower shell one energy level), shielding effects = 0.85

* Electrons in the shell deeper (left of n-1, in the shell two energy levels and lower) shielding effects = 1.00

• 4. For d and f orbitals, electrons in the same group, shielding effects: 0.35, while the electrons to the left (in all lower energy levels), shielding effects: 1.00

Elements with atomic numbers 1-18 lie in periods 1 through period 3

If we want to calculate the smallest effective nuclear charge, then we determine the electron configuration of each element

Logically, with the smallest atomic number, the H atom will have the smallest Z eff

Configuration of H element

H: 1s¹

Z = 1

S = 0

Z eff = Z - S = 1-0 = 1

So the valueof Z eff = Z

 

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