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)

Comments

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)

Physical significance of sie and sie^2

Physical significance of sie and sie^2 The wave function sie has no physical significance, it simply represents amplitude of wave while square of amplitude sie^2 represent intensity of electron. i. e sie ^2 gives probability of finding the electron in space .p the space is called atomic orbital A zero value of sie^2 means probability of finding the electron is zero and high value of sie^2 means greater chances of finding the electron . the value of sie^2 lies between 0&1. if sie^2 =1 100℅ sie^2=0 0℅

Chemistry

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