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Explain about the shape of orbitals.

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Orbital: The solution to Schrodinger equation gives the permitted energy values called eigen values and the wave functions corresponding to the eigen values are called atomic orbitals.

Shape of orbital: 

s – orbital: 

For Is orbital, l = 0, m = 0, f(θ) = 1√2 and g(φ) = 1/ √2π. Therefore, the angular distribution function is equal to 1/√2π. i.e. it is independent of the angle θ and φ. Hence, the probability of finding the electron is independent of the direction from the nucleus. 

So, the shape of the s orbital is spherical.

p – orbital: 

For p orbitals l = 1 and the corresponding m values are -1, 0 and +1. The three different m values indicates that there are three different orientations possible for p orbitals. These orbitals are designated as px , py and pZ

The shape of p orbitals are dumb bell shape.

d – orbital: 

For ‘d’ orbital 1 = 2 and the corresponding m values are -2, -1, 0, +1,+2. The shape of the d orbital looks like a clover leaf. The five m values give rise to five d orbitals namely dxy , dyz , dzx , dx2 - y2 and d The 3dz2 orbitals contain two nodal planes.

f – orbital :

For f orbital, 1 = 3 and the m values are -3, -2,-1, 0, +1, +2, +3 corresponding to seven f orbitals,

They contain 3 nodal planes.

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