Angular wave function, limitations of slater's rule

Angular wave function:

Wave function depends upon quantum no. l, m and often referred to atomic orbital.

the shape of these orbital depends upon angle 𝟅 and ⲫ.

Mathematical expression for angular wave function for s & p orbital is given

orbital Angular wave function

s (1/4π) ^1/2

pz (3/4π) ^1/2 cos 𝟅

px (3/4π) ^1/2 sin 𝟅 cos 𝟅

py (3/4π) ^1/2 sin 𝟅 sinⲫ.

the expression for s orbital has no. angle dependence ,hence s orbital are speherical symmetrical.

limitation of slater's rule

1.it is observed that slater's rule becomes less reliable for atoms of heavier elements.

2. s & p orbital are grouped together for calculating effective nuclear charge.

3.while due to higher penetration s- orbital should screen more than the orbital .

4.all electrons in shell lower than (n-1) shielded the outer electron with equal contribution(1.00) this not seen to be true.

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Radial probability distribution for p and d orbital, radial wave functions

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Linear combination of atomic orbital, Molecular orbital theory, Difference between bonding & anti bonding moleculer orbital.

Linea combination of atomic orbital molecular orbital are formed by combination of atomic orbital if ꌏ(A) andꌏ(B) are the wave function of atomic orbital of two combining atomic A and B then according to Linea combination of atomic orbital, these two wave function can be added or can be substracted .that means there are two modes of interaction (symmetric and antisymmetric) We know ꌏ(s) = ꌏ(A) +ꌏ(B) ꌏ(a) = ꌏ(A)- ꌏ(B) ꌏ(s) and ꌏ(a) represent wave function of bonding and antibonding moleculer orbital. the formation of moleculer orbital ꌏ(s) and ꌏ(a) from two atomic orbital ꌏ(A) and ꌏ(B) is represented as Molecular orbital theory (MO) theory: main points of mo theory are: 1.whwn atomic orbital combine they formed molecular orbital. 2.Number of molecular orbital formed is equal to number of atomic orbital combine. 3.atomic orbital are uninuclear while molecular orbital are polynuclear. 4.The various molecular orbital are arranged in order of in increas

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