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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