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

Radial probability distribution for p and d orbital

Radial and Angular wave function:
the radial part of wave function depends upon quantum no. n and l and gives the distribution of electron w. r. t distance .it is governed mainly exponential term

e^-Zr/na°(a not)

here

e based on natural log.
Z Atomic number
r distance from nucleus
n principal quantum no. or radial quantum no.
a° 0.529A° for hydrogen ( Bohr radii)

the exact mathematical expression for radial part of wave function for 1s or 2s and 2p orbitals.

n= 1 ,l=0
s orbital
R(r) =2× (z/a°) ^3/2 ×(2-zr/a°) ×e^-zr/2a°

n= 2 ,l=0
2s orbital
R(r) = (z/a°) ^3/2 ×(2-zr/a°) ×e^-zr/2a°

n= 2 ,l=1
2p orbital
R(r) = 1√3×(z/2a°) ^3/2 ×(zr/a°) ×e^-zr/2a°

the radial wave function can be represented by plotting radial function R(r) apart distance(r)

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Radial probability distribution curves

Radial probhjjhajajbability distribution curves: The probability of finding the electron is given by the quantity sie^2.By radial probability us probability of finding the electron within small Radial space around the nucleus. volume of spherical shell between radius r and r+dr =4πr^2 and probability of finding the electron will be 4πr^2dr sie^2. radial probability distribution curves are obtained by plotting radial probability at various distance from the nucleus . 1.Radial probability distribution curves for S orbital n=1, l= 0. distance from nucleus here A° is called angstrom. the probability of finding of electron in a shell is maximum at distance r=r° (r not) which is 0.529 A° for H atom. diagram shows that probability plot for 2s has(two region of high probability) or (two peaks) separated by node. we conclude that no. of high probability region in S orbital = n no. of node = ( n-1)

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 a...

Chemistry

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